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NEW MANUAL 



ELEMENTS OE ASTRONOMY. 



DESCRIPTIVE AND MATHEMATICAL: 



COMPRISING 



THE LATEST DISCOVERIES AND THEORETIC VIEWS, 



WITH DIRECTIONS FOE THK 



USE OF THE GLOBES, AND FOE STUDYING THE CONSTELLATIONS. 



HENRY KIDDLE, A.M., 

ASSISTANT SUPERINTENDENT OF SCHOOLS, NEW YOKX. 




/° NEW YORK: 

1YISON, PHINNEY, BLAKEMAN & Co., 

CHICAGO: S. C. GRIGGS & CO. 

1868. 



i 



Entered, according to Act of Congress, in the year 186T, by 

HENRY KIDDLE 

In the Clerk's Office of the District Court of the United States for the Southern 

District of New York. 



. 



Electrotyped by Smith & McDougai., 82 and 84 Beekman St., N. Y. 



PREFACE 



This work is designed to take the place of the " Manual 
of Astronomy," published by the author in 1852. Li method 
of treatment it is entirely new, and is much more compre- 
hensive than the previous work, containing a fuller expo- 
sition of elementary principles, and embodying the chief 
results of astronomical research during the last fifteen 
years,— a period exceedingly fruitful in discovery. 

The plan is as far as possible objective, in a proper sense ; 
that is, it is based upon the conceptions of the pupil ac- 
quired by an actual observation of the phenomena of the 
heavens, to which his attention is constantly directed ; the 
relation between these phenomena and the facts inferred 
from them being clearly shown at every step. Great pains 
have been taken to divest that part of the subject which 
treats of the Sphere of its usual arbitrary and complex 
character by developing the requisite ideas before present- 
ing formal definitions. 

Simplified methods of computing the numerical elements, 
such as periods, distances, and magnitudes, are given 
throughout the work ; in most cases the calculations being 
made lor the pupil, but without recourse to any other than 
elementary arithmetic and the most rudimental principles 
of geometry. These calculations are based on the recent 



IV PREFACE. 

determination of the solar parallax, and other elements aa 
established by the latest observations and researches of dis- 
tinguished astronomers ; and it is believed that, presented 
in this way, they will prove valuable as arithmetical exer- 
cises, as well as an important aid in imparting clear, correct, 
and permanent conceptions of the astronomical truths. 

Brief historical sketches of the various discoveries — a 
most fascinating part of the subject — are given in connection 
with the facts to which they relate. These, with all other 
matter designed to elucidate or exemplify the text, are 
printed in smaller type, and in distinct paragraphs, which 
have been distinguished by letters, so as to be readily refer- 
red to, and conveniently indicated by the teacher in assigning 



The Problems for the Globes have been placed in connection 
with that part of the text to which they refer and in which 
they are designed to exercise the pupil. 

The illustrations are copious, and have been engraved 
specially for this work, many from original drawings and 
diagrams ; the telescopic views, from drawings and photo- 
graphs made by distinguished observers. All the important 
English astronomical works of recent date have been 
carefully consulted. 

The author hopes that this little volume, containing as it 
does a full exposition of the recent progress and present 
condition of the sublimest of all sciences, will prove a 
useful and acceptable addition to the educational facilities 
so copiously supplied at the present time. 

New, Yobx, January 15, 1868. 



ooisrTEisrTs 



INTRODUCTION. 

PACT 

Mathematical Definitions 9 

CHAPTER I. 

THE HEAVENLY BODIES — GENERAL PHENOMENA. 
Apparent Motions — Copernican and Ptolemaic Systems — Classification of the 
Heavenly Bodies IT 

CHAPTER II. 

THE PLANETS. 
Their Number— Classification— Direction of their Motion 22 

CHAPTER III. 

MAGNITUDES OF THE SUN AND PLANETS. 

Their comparative Volume, Mass, and Density. Terrestrial and Major Planets 
compared 24 

CHAPTER IV. 

ORBITAL REVOLUTIONS OF THE PLANETS. 

Centripetal and Centrifugal Forces— Kepler's Laws — Comparative Eccentricities of 
the Planetary Orbits — Their Inclinations — Mean and True Place— Nodes 28 

CHAPTER V. 

DISTANCES, PERIODIC TIMES, AND ROTATIONS OF THE 
PLANETS. 

Bode's Law— Hourly Orbital Velocities— Inclination of the Planetary Axes— Times 
of Rotation — Sun's Rotation ....... 88 



VI CONTENTS. 

CHAPTEE VI. 

ASPECTS OF THE PLANETS. 

PAGE 

Angular Distance— Synodic and Sidereal Periods— Morning and Evening Star- 
Questions for Exercise 43 

CHAPTEE VII. 

THE EAKTH. 

Proofs of its sphericity 49 

section I. — Latitude and Longitude— Difference of Time— Problems for the Globe. '* 

section II. — The Hobizon— Positions of the Sphere— Paballax— Refraction 64 

bKOTion III. — Appabent Motions of the Sun and Planet6— Daily Phenomena — 

Apparent Annual Motion — Obliquity of the Ecliptic — Signs of the Ecliptic — 

Zodiac— Pbecession — Problems for the Globe 63 

Section IV. — Day and Night — Longest and Shortest Days and Nights — Constant 

Day and Night — Twilight — Problems for the Globe 73 

Section V.— The Seasons— Motion of the Line of Apsides— Zones 82 

Section VI. — Figube and Size of the Eabth — Proofs of its Oblateness— Cause 

of Precession 88 

Section VII.— Time — Solar and Sidereal Day — Equation of Time — Sidereal and 

Tropical Year— Anomalistic Year — Questions for Exercise 92 

CHAPTEE VIII. 

THE SUN. 

Its Distance— Magnitude — Rotation — Spots — Theories as to its Physical Constitu- 
tion—Light and Heat — Motion of the Sun and System in Space— Zodiacal Light 99 

CHAPTEE IX. 

THE MOON. 

Its Distance — Eccentricity — Magnitude— Phases— Sidereal and Synodical Month- 
Harvest Moon — Rotation — Orbit — Libration — Position of the Axis — Lunar Day 
and Night— Atmosphere— Selenography — Lunar Mountains — Lunar Irregu- 
larities 112 

CHAPTEE X. 

ECLIPSES. 

Cause of Eclipses — Solar and Lunar Ecliptic Limits — How to calculate them— 
Number of Eclipses — Length of Shadows of the Earth and Moon — Breadth of 
• the same — Total and Partial Eclipses — Cycle of Eclipses— Phenomena pre- 
sented by Total Eclipses — Occultations ,........:.. 131 



CONTENTS. Til 

CHAPTER XL 

TIDES. 

PAGE 

Attraction of the Sun and Moon— Relative amount calculated— Spring and Neap 
Tides — Why the Tides rise later each day — Solar and Lnnar Tide-Wares — 
Primitive and Derivative Tides — Velocity of Tide- Wave— Atmospheric Tides. 142 

CHAPTER XII. 

INFERIOR PLANETS. 

Mebctjby— Distance calculated— Diameter, Mass, etc.— Rotation— Sidereal and Sy- 
nodic Periods — Light and Heat — Seasons — Transits. Venus — Phases- 
Distance— Magnitude — Mass— Rotation — Mountains— Atmosphere — Axis— Sea- 
sons — Transits — Solar Parallax — Apparent Motions. 149 

CHAPTER XIII. 

SUPERIOR PLANETS. 

Maes— Phases — Apparent Motions — Distance— Parallax — Period— Magnitud e — Sea- 
sons—Telescopic Appearances. Jttpiteb— Period — Figure — Volume, Mass, 
etc.— Belts— Satellites— Velocity of Light. Satcen— Orbit— Period— Figure 
—Volume, Mass, etc. — Axis — Seasons— Belts — Rings— Satellites. Ubanttb — 
History of its Discovery— Distance— Orbit— Period— Magnitude— Satellites. 
Neptune— History of its Discovery — Distance, Period, etc.— Satellite. .... 168 

CHAPTER XIV. 

MINOR PLANETS. 
Their Discovery— Distance— Orbits— Periods— Origin— Nebular Hypothesis 199 

CHAPTER XV. 

MUTUAL ATTRACTIONS OF THE PLANETS. 

"Problem of Three Bodies"— Elements of a Planet's Orbit— Heliocentric and 
Geocentric Place— Variable and Invariable Elements— Great Inequality of 
Jupiter and Saturn — Centre of Gravity— Comparative Masses of the Sun and 
Planets 204 



VI11 CONTENTS. 

CHAPTER XVI. 

COMETS. 

PA<3« 

Appearance— Orbits— Elements— Elliptic Comets of Long and Short Periods- 
Velocity of Comets— Number of Comets — Size — Masses and Densities— Tails of 
Comets— RkmakkableCometb— Comet of 1680 — Halley' s Comet — Encke' s Ccmet 
— LexelTs Comet — Comet of 1811— Comet of 1843— Donati's Comet— Recent 
Comets ,. 209 

CHAPTER XVII. 

METEORS OR SHOOTING STARS. 

Star-Showers — Meteoric Epochs— Nature and Origin of Meteors— Their Number — 
Fire-Balis — Aerolites — Meteoric Dust — November Meteors— Meteors and Com- 
ets compared 223 

CHAPTER XVIII. 

THE STARS. 

Appearance— Parallax and Distance— Apparent Magnitudes — Number— Constella- 
tions How named — Names of Stars— Classification of the Constellations- 
History of each— Table showing their Relative Positions — Star-Names— List of 
Principal Stars— Problems for the Celestial Globe — Star-Figures — Change In 
the apparent places of the Stars — Nutation— Aberration of Light — Galaxy or 
Milky Way— Galactic Circle and Poles — Proper Motion of the Stars — Motion 
of Solar System in Space— Central Sun Hypothesis — Multiple Stars— Double 
Stars— Colored Stars— Binary Stars— Dimensions of Stellar Orbits— Masses of 
the Stars— Their Physical Constitution— Spectrum Analysis— Variable Stars- 
Temporary Stars— Star-Clusters .229 

CHAPTER XIX. 

NEBULA. 

History of their Discovery— How distinguished from Clusters— Resolvable and 
Irresolvable Nebulae— Herschers Nebular Hypothesis— Classification of Nebulae 
—Elliptic Nebulae— Annular Nebula?— Spiral Nebulae— Planetary Nebulae- 
Stellar Nebulae and Nebulous Stars— Irregular Nebulae— Variable Nebulae- 
Structure of the Universe 263 






INTRODUCTION 



MATHEMATICAL DEFINITIONS. 

1. Astronomy * is that branch of science which treats of 
the heavenly bodies ; as the sun, moon, stars, comets, etc. 

Before even the simple elements of this science can he learned, it is 
necessary that the rudiments of geometry should he understood ; hence, 
the following definitions are here presented as an introduction. For con- 
venience of treatment, more are, however, inserted in this section than the 
student will need, at first, to apply. The teacher should, therefore, not 
only see that they are learned by way of preparation for the general subject, 
but be careful to recur to them, when the pupil reaches the parts of the 
subject to which they specially refer. 

2. Extension, or magnitude, may be measured in three 
directions ; namely, length, breadth, and thickness. These 
are therefore called the dimensions of extension. 

a. Length is the greatest dimension ; Thickness, the shortest ; 
Breadth, the other. 

3. A Line is that which is conceived to have only one 
dimension. 

a. Lines have no real existence independently of extension, or solidity. 
They are purely abstract or imaginary quantities : the marks called 
lines are only representatives of them. 

4 A Straight Line is a line that does not change its 
direction at any point. 



* Derived from the Greek words Astron, meaning a star, and Nomos, 
meaning a law. 

Questions. — 1. What is astronomy ? 2. How may extension be measured? a. Length, 
breadth, and thickness, — how distinguished ? 3. What is a line ? a. Have lines any 
real existence ? 4. What is a straight line ? 



10 



MATHEMATICAL DEFINITIONS. 



5. A Cukve Line is one that changes its direction at 
every point. 

6. A Point is that which is conceived to have no dimen- 
sions, bnt only position. 

a. A point is represented by a dot ( . ). 

b, A straight line measures the shortest distance between two points. 

7. A Surface is that which is conceived to have two 
dimensions, length and breadth. 

8. A Plane Surface, or Plane, is a surface with which, 
if a straight line coincide in two points, it will coincide 
in all. 

a. That is, a straight line cannot lie partly in a plane, and partly 
out of it ; and if applied to it in any direction, it will coincide with it 
throughout its whole extent. The term plane does not imply any 
limitation, or boundary, but signifies indefinite direction, without 
change, both as to length and breadth. 

9. A plane bounded by lines is called a Plane Figure. 

10. A Circle is a plane figure bounded 
by a curve line every point of which is 
equally distant from a point within, 
called the centre. 

11. The curve line that bounds a cir- 
cle is called the Circumference. 

12. The Diameter of a circle is a 
straight line drawn through its centre 

from one point of the circumference to another. 

13. The Kadius is a straight line drawn from the centre 
to the circumference. 

14. An Arc is any part of the circumference. 

Questions.— 5. What is a curve line? 6. A point? a. How represented ? b. The 
shortest distance between two points? T. What is a surface? 8. A plane surface? 
a. Does the term plane imply any limit? 9. What is a plane figure? 10. What is a 
circle ? 11. What is meant by the circumference 1 12. The diameter ? 13. The radius ? 
14. What is an arc ? 



Pig. 1. 
Tangent 


«/ Diaia/fetcr 


«y\ Semi 

i 


circle / 



MATHEMATICAL DEFINITIONS. 



li 



15. A Tangent is a line which touches the circumference 
in one point. 

16. A Semiciecle is one-half of a circle ; a Quadrant is 
a quarter of a circle. 

17. The circumference of a circle is supposed to be divided 
into 360 degrees, each degree into 60 minutes, and each 
minute into 60 seconds. 

a. Degrees are marked ( ° ) ; minutes, ( ' ) ; and seconds, ( " ). 

18. An Angle is the difference in direc- 
tion of two straight lines that meet at a 
point, called the vertex. 

a. It is of the greatest importance that the student 
of Astronomy should form a clear idea of an angle, 
since nearly the whole of astronomical investigation is based upon it. 
The apparent distance of two objects from each other, as seen from a 
remote point of view, depends upon the difference of direction in which 
they are respectively viewed ; that is to say, the angle formed by the 
two lines conceived to be drawn from the objects, and meeting at the 
eye of the observer. This is called the angular distance of the objects, 
and, as will readily be understood, increases as the two objects depart 
from each other and from the general line of view. 



Pig. 3. 









19. The Angle of Vision, or Visual Angle, is the 



Questions.— 15. What is a tangent ? 16. A semicircle ? A quadrant ? 17. How 
is the circumference conceived to he divided ? a. How are degrees, minutes, and 
seconds marked? 18. What is an angle? a. Its importance in astronomy? What is 
angular distance ? 19. What is the angle of vision ? 



12 



MATHEMATICAL DEFINITIONS. 



angle formed by lines drawn from two opposite points of a 
distant object, and meeting at the eye of the observer. 

a. It will be easily seen that, as the apparent size of a distant object 
depends upon the angle of vision under which it is viewed, it must 
diminish as the distance increases, and vice versa. 

Thus, the object A B (Fig. 3) is viewed under the angle A P B, which 
determines its apparent size in that position ; but when removed farther 
from the eye, as at C D, the angle of vision becomes C P D, an angle ob- 
viously smaller than A P B, and hence the object appears smaller. At E F, 
the object appears larger, because the visual angle E P F is larger. The 
farther the object is removed, the less the divergence of the lines which 
form the sides of the angle ; and the nearer the object is brought to the eye, 
the greater the divergence of the lines. 

20. An angle is measured by drawing a circle, with the 
vertex as a centre, and with any radius, and finding the 
number of degrees or parts of a degree, included between 
the sides. 

21. A Eight Angle is one that con- 
tains 90 degrees, or one-quarter of the 
circumference. 

22. When one straight line meets an- 
other so as to form a right angle with it, 
it is said to be perpendicular. 

23. A straight line is said to be per- 
pendicular to a circle when it passes, or 
would pass if prolonged, through the 
centre. 

24. An angle less than a right angle is 
called an Acute Angle; one greater 
than a right angle is called an Obtuse 
Angle. 



Fig. 4. 



# 



tf 



Fig. 5. 




Fig. 6- 




Questions.— a. How dependent on the distance of an object? Explain from the dia- 
gram. 20. How is an angle measured ? 21. What is aright angle? 22. When is one 
line perpendicular to another? 23. When is a straight line perpendicular to a circle ? 
24 What is an acute angle ? An obtuse angle ? Illustrate by Fig. 7. 



MATHEMATICAL DEFINITIONS. 



13 



Fig. 7- 




^B 



In the annexed diagram, the semi-cir- 
cumference is used to measure all the 
angles having their vertices, or angular 
points, at C. Thus BCD, containing 
the arc B D, is an angle of 45° ; B C E, 
an angle of 90° ; and BCF, of 120°. 
The points A and B are at the angular 
distance of 180°, or two right angles 
from each other. 



25. A Tkiangle is 
bounded by three sides. 



a plane figure 



Fig. 8. 




Parallel Lines . 



Fig. 11. 



a. The sum of the three angles of every trian- 
gle is equal to two right angles. 

b. A triangle that contains a right angle is 
called a Right-angled Triangle. 

c. A triangle having equal sides is called an 
Equilateral Triangle. 

d. Each of the angles of an equilateral triangle 
is an angle of 60° ; since the three angles are 
equal to each other, and their sum is equal to 
180°. 

26. Paeallel Lines are those situ- 
ated in the same plane, and at the same 
distance from each other, at all points. 

a. Parallel lines may be either straight or 
curved. 

b, The circumferences of concentric circles, 
that is, circles drawn around the same centre, are 
parallel. 

27. An Ellipse is a curve line, from any point of which 
if straight lines be drawn to two points within, called the 
foci, the sum of these lines will be always the same. 

Qttestions. — 25. What is a triangle ? ft. Sum of its three angles ? b. What is a right- 
angled triangle ? c. An equilateral triangle ? d. The value of each of its angles ? Why ? 
26. What are parallel lines? a. Are they always straight? 6. When are circles par- 
allel ? 27. What is an ellipse ? 




u 



MATHEMATICAL DEFINITIONS. 





E 
i / 

1/ 


s\ A 




F ^-^ 


|F I 



Pig. 12. The curve line D B E G represents 

an ellipse, the sum of the two straight 
lines drawn to F and F, the foci, from 
the points A, B, and C, respectively, 
being always equal. This sum is equal 
to the longest diameter, D E. 

28. The longest diameter of 
an ellipse is called the Ma joe * 
Axis ; f and the shortest diam- 
eter, the Minor* Axis. 

In the diagram, D E is the major axis, and B G the minor axis. 

29. The distance from either of the foci to the centre of 
the ellipse is called the Eccentricity J of the ellipse. 

a. It will be readily seen that the greater the eccentricity of an 
ellipse, the more elongated it is, and the more it differs from a circle ; 
while, if the eccentricity is nothing, the two foci come together, and 
the ellipse becomes a circle. 

b. The distance from the extremity of the minor axis to either of the 
foci is always equal to one-half of the major axis. 

In the above diagram, F O is the eccentricity, and B F is equal to D O. 
The amount of eccentricity of any ellipse is ascertained by comparing it 
with one-half the major axis. Thus, in the diagram, O F being about one 
half of O D, the eccentricity of the ellipse may be nearly expressed by .5. 

30. A Sphere, or Globe, is a round body eyery point of 
the surface of which, is equally distant from a point within, 
called the centre. 

31. A Hemisphere is a half of a globe. 

32. The Diameter of a sphere is a straight line drawn 



* Major and Minor are Latin words, meaning greater and less. 
t A Latin word meaning an axle, that on which any thing turns. 
% From the Greek, ec, from, and centron, the centre. 

Questions.— 28. What is the major axis? The minor axis? 29. What is meant by 
eccentricity? a. What does it show ? b. Distance of foci from the extremity of minor 
axis? Explain from the diagram. 30. What is a sphere ? 31. A hemisphere ? 82. The 
diameter of a sphere ? 



MATHEMATICAL DEFINITIONS. 



15 




- 



Fig. 14. 



through the centre, and ter- Fi s- 1S - 

minated both ways by the sur- 
face of the sphere. 

33. The Kadius of a sphere is 
a straight line drawn from the 
centre to any point of the surface. 

34. Circles drawn on the sur- 
face of a sphere are either Great 
Circles or Small Circles. 

35. Great Circles are those 
Whose planes divide the sphere 
into equal parts. 

36. Small Circles are those whose planes divide the 
sphere into unequal parts. 

37. The Poles of a Circle 
are two opposite points on the 
surface of the sphere, equally dis- 
tant from the circumference of 
the circle. 



a. The poles of a great circle are, of 
course, 90° distant from every point 
of its circumference. 

b. Two circles of the sphere are par- 
allel when they are equally distant from each 
other at every point. 

c. Two circles are perpendicular to each other 
when their planes are perpendicular, or at right 
angles with each other. 

d. The Plane of a Circle or any other figure 
is the indefinite plane surface on which it may 
be conceived to be drawn. 




PEEPENDICXTLAB PLANES. 
Fig. 15. 




PLANES OF GEEAT CIECLES. 



Questions. — 33. What is the radius f 34. How are circles of the sphere divided \ 
85. What are great circles ? 36. Small circles ? 37. Poles of a circle ? a. Poles of a 
great circle ? b. When are circles of the sphere parallel ? c. When perpendicular ? 
d. What is meant by the plane of a circle ? 



16 



MATHEMATICAL DEFINITIONS. 



38. A Sphekoid * is a body resembling a sphere. 
Fig 16> 39. There are two kinds of spheroids ; 

.. - -v Oblate and Peolate Spheroids. 

40. An Oblate Spheroid is a sphere 
flattened at two opposite points, called the 
poles. 

41. A Prolate Spheroid is a sphere 
oblIteTp'hekoid. extended at two opposite points. 

Thus, an orange is a kind of oblate spheroid ; and an egg, a kind of 
prolate spheroid. 




* Spheroid means like a sphere. Oid is from the Greek word eido, mean- 
ing to resemble. 

Questions.— 38. What is a spheroid ? 39. How many kinds of spheroids ? 40. What 
Is an oblate spheroid ? 41. A prolate spheroid ? 



&A 






CHAPTER I. 

THE HEAVENLY BODIES— GENERAL PHENOMENA. 

1. The Sun, the Moon, and the Stars, are the most 
conspicuous bodies of which astronomy treats. 

a. Antiquity of the Science. — The various appearances presented 
by these bodies must always have engaged the attention of mankind. 
The sublime spectacle of the starry heavens would naturally, in the 
earliest times, excite the admiration of the most careless or ignorant 
observer; and the curiosity of mankind would be early aroused to 
ascertain the nature of those " refulgent lamps " which lend so much 
splendor and beauty to the otherwise sombre gloom of night. 

Hence, we find that astronomy is a very ancient science. The shep- 
herds of Chaldea,* and the priests of Egypt and India, had, in remote 
antiquity, made some progress in astronomical discovery ; and, it is 
said, Chinese observations are on record that date back more than 
1000 years before Christ. 

b. Ordinary Phenomena. — The most obvious phenomena f con- 
nected with these bodies are their rising and setting, and their 
constant motion in the same general direction from one side of the 
heavens to the other ; and consequently these appearances were prob- 
ably among the first that incited to scientific inquiry. 

c. The Earth's Rotation. — The simple fact that the earth — the 
body on which we are placed — turns round once every twenty-four 
hours, clears away all difficulty in explaining these daily appearances ; 
but it was not until comparatively recent times that mankind could be 
brought generally to accept this truth. 

As late as 1633, it was deemed irreligious to believe in the motions 



* A country of antiquity, situated between the Euphrates and Tigris 
rivers, 
t Phenomena, plural of phenomenon, a Greek word meaning an appearance. 

Questions. — 2. Which are the most conspicuous of the heavenly hodies ? a. Astron- 
omy—why an ancient science ? b. What are the most ohvious phenomena ? c. The 
earth's rotation — what does it explain ? Galileo ? 



18 THE HEAVENLY BODIES. 

of the earth ; and Galileo, in his seventieth year, was imprisoned, and 
finally compelled to acknowledge himself as guilty of error and heresy 
in teaching this astronomical truth. 

d. The Stars appear to keep very nearly the same situations with 
respect to each other ; and hence were called Fixed Stars, to distin- 
guish them from other bodies which resemble, in their general appear- 
ance, stars, but seem to move about in the heavens, at one time being 
near one star, then another, now moving in one direction, then in 
another ; thus, as it were, wandering about in the heavens. For this 
reason, such bodies were called planets, or wandering stars. 

[In the Greek language, planetes means a wanderer. The term fixed stars 
is now but little used by astronomers ; and in this work, when the term 
stars is used, it is intended to designate fixed stars.] 

2. The apparent motions of the sun, planets, and stars 
are explained by supposing, 1. That the earth is a sphere, or 
nearly so ; 2. That it turns on its axis ; 3. That the earth 
and planets revolve around the sun; and, 4. That the stars 
are situated at an immense distance from the sun and 
planets, in the regions of space, — a distance so vast that their 
movements with respect to each other can not generally be 
discerned. 

3. The sun with all the bodies revolving around it, is 
called the Solar* System. 

a, Oopernican System. — This arrangement of the sun in the centre 
with the planets revolving around it, is sometimes called the Coper- 
nican System, from Nicholas Copernicus, who, in 1543, revived the doc- 
trine taught by Pythagoras, a Greek philosopher, more than 2,000 
years before, that the sun is the central body, and that the earth and 
planets revolve around it. 

b. Ptolemaic System. — Previous to Copernicus, the general belief, 
for more than two thousand years, had been that the earth is the cen- 



* From the Latin word Sol, meaning the sun. 



Questions. — d. Stars and planets — how distinguished? What does planet mean? 
2. How are the apparent motions of the sun, planets, and stars explained ? 3. What is 
the solar system ? a. The Copernican system— why so called ? Pythagoras ? 6. Tha 
Ptolemaic system— why so called ? Describe it.. 



20 



THE HEAVENLY BODIES. 



tre of the universe, and that all the other bodies revolve around it, in 
the following order: the moon, then the sun and planets in their 
order, and then the stars. Each of these bodies was conceived by 
Aristotle to be set in a hollow, crystalline sphere, perfectly transparent, 
by which it was carried around the earth and prevented from falling 
upon it. This celebrated system is very ancient, but being advocated 
and illustrated by Ptolemy, an eminent astronomer who flourished at 
Alexandria, in Egypt, about 140 a.d., it was subsequently called the 
Ptolemaic System. 

c. The Invention of the Telescope. — The doctrine of Copernicus, 
as promulgated in his great work, styled the "Revolutions of the 
Celestial Orbs," published in 1543, was at first generally rejected, and 
despised as visionary and absurd ; but the invention of the telescope, in 
1610, and the discoveries made by means of it, by Galileo and others, 
afforded abundant evidence of the truth of this hypothesis. 
Fig. 17- 

4. Planets are bodies that re- 
volve around the sun. 

5. The path in which we may 
conceive a planet to revolve is 
called its or hit 

6. The planets all revolve around 
the sun in the same direction, in 
orbits nearly circular, and situated 
in nearly the same plane. 




a planet's orbit. 
Fig. 18. 




a comet's obbit. 



a. Comets' Orbits. — In these respects 
they differ from Comets, which also re- 
volve around the sun, but in different 
directions, in widely different planes, and 
in very elongated, or eccentric orbits ; 
that is, elliptical orbits of great eccen- 
tricity. [See Introduction, Art. 29.] 

I 

7. There are two kinds of planets ; 
Primary and Secondary Planets. 



Questions.— c. What is said of the telescope ? 4. What are planets? 5. What is 
the orbit of a planet f 6. How do the planets revolve ? a. Comets' orbits ? 7. How- 
many kinds of planets f 



THE HEAVENLY BODIES. 21 

8. Primary Pla*tets are those that reyolve around the 
sun only. 

9. Secondary Planets, generally called Satellites,* 
are those that revolve around their primaries, and, with 
them, around the sun. 

The moon is an example of a secondary planet. It is the earth's 
satellite, its revolution around the earth being clearly indicated by 
the changes which it undergoes each month. 

10. The Solar System is thus composed of the sun, the 
primary planets, the secondary planets, and the comets; 
while the stars are bodies situated at an immense distance 
beyond the system. 

11. All the heavenly bodies may be divided into two gen- 
eral classes; namely, Luminous Bodies and Opaque Bodies. 

12. Luminous bodies are such as shine by their own light ; 
opaque bodies are such as shine by reflecting the light of 
some luminous body. 

a. The sun is evidently a luminous body ; for we receive from it 
both light and heat, and in every position it presents a resplendent cir- 
cular surface, called its Disc. The moon is as evidently opaque, since 
it does not always exhibit an entire disc, but various portions of it at 
different times, such portions being called Phases. 

b. The stars present no disc, but only luminous points, shining with 
that twinkling light which indicates their intense brilliancy and vast 
distance. They are believed to be luminous bodies, since we can dis- 
cover no body from which they could receive their light ; and, more- 
over, the light itself which they emit has different properties from 
those possessed by reflected light. 

-c. The planets, though in general appearance resembling the stars, 
may readily be distinguished from them by their steady light. When 
viewed through a telescope, some of them exhibit phases like those 
of the moon. 

* From the Latin word satelles, (plural, satellites,) meaning a guard. 

Questions. — 8. What are primary planets ? 9. Secondary planets ? 10. Of what is 
the solar system composed ? Where are the stars situated? 11. What general divi. 
sion of the heavenly hodies ? 1 2. What are luminous hodies ? Opaque hodies ? a. Proof 
that the sun is luminous ? That the moon is opaque ? 6. Proof that the stars are 
luminous ? c. Light of planets— how distinguished from that of stars ? 



CHAPTER II. 

THE PLANETS. 

13. There are eight large primary planets in the solar 
system, besides a great number of smaller ones, called Minor 
Planets, or Asteroids.* 

14. The names of the eight large primary planets, in the 
order of their distances from the sun, are Mercury, Venus, 
the Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. 

15. All the primary planets except the earth are divided 
into two classes, inferior and superior planets. 

16. Mercury and Venus are called inferior planets, because 
they revolve within the orbit of the earth ; Mars, Jupiter, 
Saturn, Uranus, and Neptune are called superior planets, 
because they revolve beyond the orbit of the earth. Instead 
of the terms inferior and superior, interior and exterior are 
sometimes used. 

a. Vulcan. — A planet inferior to Mercury has been supposed to 
exist ; and in 1859, a French astronomer was thought by some to have 
discovered it. Later observations have not, however, confirmed, but 
rather disproved, its existence. The name given to this supposed 
planet is Vulcan. 

17. The Minor Planets are very small planets which 
revolve around the sun, between the orbits of Mars and 
Jupiter Ninety-five have been discovered (1867). 

a. These small planets were at first, and have been, very generally, 
called Asteroids ; they have also been called Planetoids. The name 

* From the Greek aster, meaning a star, and eido, to resemble. 

Questions. — 13. How many primary planets in the solar system ? 14 What are the 
names of the large planets ? 15. How divided ? 16. Which are called inferior ? Which 
superior? Why? a. Vulcan — what is said of it? IT. What are the minor planets ? 
Their number ? a. What other names are applied to them ? 



THE PLANETS. 23 

above given has, however, been extensively used by astronomers, and 
appears to be the most significant and appropriate. 

18. All the primary planets revolve around the sun in the 
direction which is designated from west to east. 

a. It is difficult to fix definitely the direction of circular motion, 
since when viewed in one position it may seem to be from left to right 
(as the hands of a clock move), and in another, from right to left. The 
motion of the planets, as we view them, is from right to left, — the reverse 
direction of the hands of a clock. This is the direction indicated in the 
diagrams of this work. 

b. East is at or near where the sun rises ; West, at or near where 
it sets. South is in the direction of the sun's place at noon ; North, 
directly opposite the south. If we stand so as to face the north, the south 
will be behind us, the east on the right hand, and the west on the left. 

19. Secondary planets, or satellites, have two motions: 
one around their primaries, and another, with them, around 
the sun. 

20. Eighteen satellites are known to exist in the Solar 
System : the earth has one, called the moon ; Jupiter has 
four ; Saturn, eight ; Uranus, four ; and Neptune, one. 

a. While Uranus is undoubtedly attended by at least four satellites, 
there is a very great uncertainty as to the exact number which belong 
to it. Sir William Herschel, by whom this planet was discovered, in 
the latter part of the last century, detected, as he thought, six satel- 
lites ; but only two of these have been observed by ether astronomers, 
which, with two others discovered by Lassell in 1853, make the four 
referred to in the text. 

21. The satellites of the earth, Jupiter, and Saturn re- 
volve around "their primaries from west to east; those of 
Uranus and Neptune, from east to west. 

u. With the exception of the satellites of Uranus, and the satellite 
of Neptune, all the planets of the Solar System revolve in the same 
direction, that is, from west to east. 

Questions. — 18. What is the direction of the planets' motion? a. How defined? 
6. What is meant hy East ? West? South? North? 19. What motions have satel- 
lites ? 20. How many are known to exist ? Enumerate them ? a. Satellites of Uranus ? 
21. In what direction do the satellites revolve ? a. What uniformity of motion in the 
solar system ? 



Fig. 19. 



CHAPTER III. 

MAGNITUDES OF THE SUN AND PLANETS. 

22. The Sun is by far the largest body in the Solar Sys- 
tem, being more than 500 times as large as all the planets 
taken together. 

23. Its diameter is a little more than 850,000 miles. 

24. The LARGEST 

planet is Jupiter, its 
diameter being 85,000 
miles, or one-tenth as 
large as that of the 
sun. 

a. Volume, Mass, 
Density. — The diameter 
of Jupiter being one-tenth 
as large as the sun's, its 
volume, or hulk, is one one- 
thousandth (.001) that of 
the sun ; since it is only 
one-tenth as great in each 
dimension, — length, 
breadth, tfnd thickness ; 
and -j^j X -jfo X j-L = y-yi- o . 

This is expressed generally by saying that solid bodies of similar shape 

are in proportion to the cubes of their like dimensions. 

b. The volume of a body is the amount of space which it occupies, 




COMPARATIVE SIZE OF SUN AND JUPITE3. 



Questions — 22. What is the comparative size of the sun? 23. Length of its diam- 
eter ? 24. Which is the largest planet ? Its diameter ? a. Comparative volume of the 
sun and Jupiter ? How found ? b. Define volume. 



SUN AND PLANETS. 25 

as indicated by its length., breadth, and thickness. The volumes of 
bodies are in proportion to the products of their three dimensions. 

c. Two bodies may be equal in volume, but contain very different 
quantities of matter, owing to the different degrees of compactness of 
their substance. Thus, a piece of cork, equal in bulk to a piece of lead, 
contains only about ^g as much matter. The quantity of matter which 
a body contains is called its mass ; the degree of compactness of its 
subtance is called its density. 

d. The mass of a body depends upon its volume and density con- 
sidered conjointly. Thus, if the volumes of two bodies are as 2 to 3, 
and their densities, as 1 to 5, their masses will be as 1 X 2 to 3 X 5, or 
as 2 to 15 ; that is to say, the mass of the second will be 7£ times as 
great as that of the first. 

25. The following are the diameters of the large primary 
planets in miles :— 

[These are given in round numbers so as to be easily remembered ; a more 
exact statement will be found in another part of this work. It is im- 
portant that the student should carefully commit to memory these num- 
bers, since the relative magnitudes of the planets form the basis of much 
of the reasoning in respect to the solar system.] 



1. Jupiter, . 


. 85,000. 


5. Earth, . 


. 7,913, 


2. Saturn, . 


. 70,000. 


6. Venus, . 


. 7,500. 


3. Neptune, 


. 37,000. 


7. Mars, , 


. 4,300. 


4. Uranus, . 


. 33,000. 


8. Mercury, 


. 3,000. 



a. Major and Terrestrial Planets.— The first four of these planets, 
it will be seen, are very much larger than the remaining four, and are, 
for this reason, sometimes called the Major Planets ; while the others, 
being in the vicinity of the earth, are sometimes called the Terrestrial 
Planets. 

b. Illustration. — A clear idea of the comparative size of the sun 
and planets may be obtained by conceiving the sun to be a globe 
two feet in diameter. Mercury and Mars would then be of the size of 
pepper-corns ; the earth and Venus, of the size of peas ; Jupiter and 

Questions.— c. What is meant by the mass of a body ? Its density ? d. On what 
does mass depend ? 25. State the diameter of each planet. Name the planets in the 
order of size. a. Which are called major planets? Terrestrial planets ? b. Give an 
illustration of the comparative size of the sun and planets. 



26 MAGNITUDES OF THE 

Saturn, as large as oranges ; and Neptune and Uranus, as large as full- 
sized plums. [See figure, page 19.] 

26. The Minor Planets, or Asteroids, are all of very 
small size, the diameter of the largest not exceeding 300 
miles, and that of the smallest being only a very few miles. 

a. Entire Mass of the Minor Planets.— It has been computed by 
the celebrated French mathematician, Le Verrier, that their entire 
mass, however many may exist, can not exceed one-fourth that of the 
earth. This calculation is based on the amount of disturbance occa- 
sioned by their united attraction, in the motions of the Earth and 
Mars. Now, the diameter of the largest being only about - 8 % of the 
diameter of the earth, its volume must be only jg^oo of the earth's ; 
and hence, it would require 4,750 planets as large as the largest of the 
asteroids to equal the amount specified by the mathematician. 

27. All the Satellites are smaller than Mars, and with 
the exception of two, one of Jupiter's and one of Saturn's, 
are smaller than Mercury. 

a. The diameter of the moon is 2,160 miles ; the four satellites of 
Jupiter, excepting one, are larger than the moon ; and the eight satel- 
lites of Saturn, excepting one, are smaller than the moon. 

28. The following presents a comparative view of the 
densities of the primary planets, as compared with that of 
water : 



1. Mercury, . 


. 6i. 


5. Jupiter, . 


■ If. 


2. Venus, 


. 51. 


6. Uranus, . 


. 1. 


3. Earth, . -\ 


• 5f. 


7. Neptune, 


9 
• TU 


4. Mars, . \ 


. 4. 


8. Saturn, . 


3 

4- 



a. It will be seen that the terrestrial planets are all of considerably 
greater density than the major planets ; and that the densities dimin- 
ish, with the exception of Saturn, as the distance of the sun increases. 

Questions. — ?6. What is the size of the minor planets? a. Their entire mass? 
2T. What is the comparative size of the satellites ? a. What, compared -with the moon ? 
28. What is the density of each of the primary planets ? a. Density of the terrestrial 
planets compared with that of the major planets? 



SUtf AND PLANETS, 



27 



29. The density of the- sun is only one-fourth that of the 
earth, or about 1^ that of water. The density of the moon 
is about 37 1 



•2 that of water. 

a* Masses of the Planets. — If we arrange the planets according to 
their mass, they will stand in precisely the same order as when 
arranged according to volume, though not in the same proportion. 
The student can verify this by applying the principle explained in 
Art. 3, d . The following table presents a general view of the com- 
parative masses of the sun and planets, expressed in approximate num- 
bers, the earth being 1 : — 







Sun, . 


. . 315,000. 






f Jupiter, . 
1 Saturn, . 


. 301. 


r Earth, . 
Terrestrial ! Venus, . 


. 1. 


Major 


. 90. 


. h 


Planets. 


Neptune, 


. 16 2 L . 


Planets. 1 Mars, . 


• h- 




*- Uranus, . 


Moon, . 


^ Mercury, 


. -iV 



Questions.— 29. What is the density of the sun and moon ? a. Comparative masses 
of the planets ? 



CHAPTER IV. 

THE OEBITAL EEVOLUTIONS OF THE PLANETS. 

30. A planet's revolution in its orbit is sustained by the 
united action of two forces ; namely, the Centripetal * and 
the Centrifugal \ forces. 

a. Laws of Motion. — No portion of matter can set itself in motion ; 
nor, when in motion, can it stop itself. Whatever sets a body in mo- 
tion, or stops it when in motion, is called Force. 

b. A body when acted upon by a single force, moves in a straight 
line ; and will continue to move in the same direction, and with the 
same velocity, until acted upon by some other force. 

Fig. 20. 




* From the Latin words centrum, meaning the centre, and peto, meaning 
to seek. 
t From the Latin words centrum, and fugio, meaning to flee from. 



Questions.— 30. "What forces sustain the planets in their orbits? a. What is force ? 
b. What is the effect of a single force ? 



ORBITAL REVOLUTIONS OF THE PLAHETS. * 29 

c. A force may be either impulsive, that is, acting once and then 
ceasing to act, or continuous, that is, acting constantly. 

d. Resultant Motion. — When a body is impelled by two forces in 
different, but not opposite, directions, it moves in a straight line be- 
tween them. This line is the diagonal of a parallelogram of which the 
lines that represent the two forces are adjacent sides. 

Thus, let A B (Fig. 20.) represent the line over which the body A would 
pass in a certain time under the influence of one force, and A C, the line 
over which it would pass in the same time, if acted upon by another force ; 
then under the simultaneous action of both forces, it will pass over the line 
A D in the same time, and continue to move in this line until acted upon by 
some third force. This line is called the resultant of the two forces. 

e. Curvilinear Motion. — If one of the two forces were a continuous 
force, the body would be drawn, at every point, from the straight line, 
and, consequently, would move in a curve line ; and these two forces 
might be so related to each other that the body would move around 
the centre of the continuous force in a circle or ellipse. In that case, 
the continuous force would be the Centripetal Force, and the impulsive 
force, the Centrifugal. 

31. The Centripetal Force is that by which a body 
tends to approach the centre, or point around which it is 
revolving. 

32. The Centrifugal Force is that by which a body 
tends to fly off from the orbit in which it is revolving. 

33. The centripetal force which acts upon the primary 
planets is the attraction of the sun ; that which acts upon 
the secondary planets is the attraction exerted by their 
respective primaries. 

34. All bodies attract each other in direct proportion to the 
mass, or quantity of matter, and inversely as the square of 
the distance. That is, a body containing twice the quantity 
of matter of another body exerts twice the force ; but, at 
twice the distance, would exert only one-fourth the force. 

Questions.— c. What different kinds of forces V d. What is the effect of two forces Y 
Explain from the diagram. Resultant? e. Curvilinear motion— how produced ? 31. De- 
fine the centripetal force. 32. The centrifugal force. 33. What force acts on the 
planets as a centripetal force i 34. State the general law of attraction. 



30 " THE OKBITAL REVOLUTIONS 

tt. Newton's Discovery. — This is the celebrated taw of universal 
gravitation discovered by Sir Isaac Newton, in 1665. It is said to have 
been suggested to his mind by the simple occurrence of an apple's 
falling from a tree. Observing that all bodies, when unsupported, fall 
toward the centre of the earth, he inferred that this must be occa- 
sioned by an attractive force exerted by the earth ; and from this, his 
mind was led to inquire whether it is not the same force, that is, a 
force acting according to the same law, which confines the moon in 
her orbit around the earth, and the earth and planets in their orbits 
around the sun. The calculations which he made proved that these 
conjectures were correct, and thus established the law. 

b. Centrifugal Force. — The centrifugal force must arise from an 
impulse originally given to the planets when they commenced their 
motions ; since, without such an impulse, they would have simply 
moved toward the sun and have been incorporated with it. And if the 
centrifugal force were now destroyed, the planets would all move in 
straight lines to the sun ; while, if the attraction of the sun were sus- 
pended,, they would move off into space in tangent lines to their orbits. 

Let A B (Fig. 20) represent the amount of the centripetal, and A C that 
of the centrifugal force, for a given time; then completing the parallelo- 
gram, and drawing the diagonal A D, we find the point which the body 
when acted on by both forces will reach in that time. E, F, and G may be 
shown in a similar way to be the points reached by the body at the end of 
successive periods of time of an equal length ; and thus, if the forces acted 
by impulses, the body would describe the broken line formed by the diag- 
onals of the parallelograms ; but as the force of gravitation is a continuous 
force, the revolving body describes a curve, which may either be a circle or 
an ellipse. 

35. The planets' orbits are ellipses, having the sun or cen- 
tral body in one of the foci. 

a, Kepler's Laws. — This is the first of the three celebrated truths 
pertaining to the planetary motions, discovered by Kepler after many 
years of investigation, and announced by him in 1609 ; hence, called 
" Kepler's Laws." Previous to this time, the general belief among 
astronomers had been that the planets' orbits are circular in form, since 

Questions. — a. By whom discovered, and how ? b. Origin of the centrifugal force ? 
Explain from diagram. 35. What is the shape of the planets' orbits ? a. By whom 
discovered ? Previous belief. 



OF THE PLACETS. 



31 



they conceived the circle to be the most perfect and beautiful of curves ; 
but, according to this theory, they had found very great difficulty in 
accounting for the irregularities in the apparent motions of the planets. 

b. The Epicycle.* — This was, however, partially accomplished 
by ingeniously supposing that the planet, instead of revolving in a 
simple orbit, revolved in a small circle, called an epicycle, the centre 
of which moved around in a circular orbit. This hypothesis was in- 
vented, it is supposed, about two centuries B. C, and was adopted by 
Ptolemy and all the great astronomers, including Copernicus himself, 
who could not account for the apparent irregularities in the motions 
of Mars, which has a very eccentric orbit, on any other hypothesis. 
The explanation by the epicycle is illustrated by the annexed diagram. 

The small circle represents Fig. 21. 

the epicycle, the centre of which 
moves in the large circle around 
the sun, S. At A the planet is 
nearest to the sun ; hut while it 
performs one-quarter of a revo- 
lution in the epicycle, the latter 
also moves over one-quarter of 
its orbit, and thus the planet is 
carried to B, and in a similar 
manner to C, its farthest point 
from the sun, and thence through 
D to A again. The difference 
between its greatest distance 
from the sun C S, and its least 
distance A S, is equal to the di- 
ameter of the epicycle. epicycle. 

c. Tycho Brahe. — Such ingenious but cumbrous hypotheses could 
only be sustained by the most imperfect observations made with the 
rudest instruments ; but when astronomy, as an art of observation, 
came to be cultivated, they were necessarily exploded. Tycho Brahe 
is justly to be considered the founder of modern practical astronomy. 
He was born in 1546, in Sweden, and so great a reputation did he 




* From the Greek words epi, meaning upon, and cycle, a circle 
circle upon a circle. 



that is, a 



Questions.— 6. What is the hypothesis of the epicycle ? Explain by the diagram. 
c. Tycho Brahe ? Value of his labors, and use made of them by Kepler ? 



32 THE ORBITAL REVOLUTIONS 

acquire, that Ferdinand, king of Denmark, built for him, on an island 
at the mouth of the Baltic, a magnificent observatory, which he styled 
" Uraniberg, or the City of the Heavens." His accurate observations 
of the planets were the means of conducting Kepler to the discovery 
of his famous laws. No less than nineteen different hypotheses were 
made by Kepler, before he could bring his mind to abandon the theory 
of the circular motion of the planets, and then he assumed the ellipse, 
as being the next most beautiful curve. The adoption of this hypo- 
thesis at once reconciled the computed with the observed place of Mars ; 
and, on applying it to the other planets, he found still more convincing 
proof of its truth. 

36. The straight line that joins the sun or central body 
with the planet at any point of its orbit, is called the Radius- 
Vector* 

37. The point of a planet's orbit nearest to the sun is 
called its Perihelion ; f the point farthest from the sun, its 
Aphelion.J 

€1, Apsides. — The aphelion and perihelion are,, of course, the ex- 
tremities of the major axis. These two points are sometimes called its 
Apsides,% and the line that joins them, the Line of Apsides. 

b. One-half of the sum of the aphelion and perihelion distances of a 
planet is, of course, the mean distance. This is always equal to the 
distance of a planet from the sun when it is at either extremity of its 
minor axis. [See Introduction, Art. 29, &.] 

38. The radius-vector of a planet's orbit passes oyer equal 
spaces in equal times. This is the second of Kepler's laws. 

If S (Fig. 22) represent the sun in the focus of a planet's elliptical orbit, A 
will be the aphelion, P the perihelion, and A S, B S, C S, etc., the radius- 



* Vector, in the Latin, means that which carries. The radius-vector io con- 
ceived to carry the planet as it moves around in its orbit. 
t From the Greek pen, meaning around or near ; and helios, the sun. 
% From apo, meaning/rom, and helios. Apo in combination becomes aph. 
% Apsis, plural apsides, is from the Greek, and means & joining. 



Questions. — 36. Define radius-vector. 37. Define perihelion and aphelion, a. Ap- 
sides and apsis line, b. What is mean distance? 38. What is Kepler's second law? 
Explain from the diagram. 



OF THE PLANETS. 



33 




vector in different positions of the plan- 
et. The planet moves in its orbit so 
that the spaces A S B, B S C, etc., may 
be equal, if described in equal times. 
It has therefore to move much faster 
in the perihelion than in the aphelion, 
since at the former point the spaces p 
must be wider in order to make up 
for their diminished length. 

a. Orbital Veloctiy.— The ve- 
locity of a planet must therefore be 
variable when it moves in an ellip- 
tical orbit, being greatest at the 

periheliqn, least at the aphelion, and alternately increasing and dimin- 
ishing between these points. 

b, The second law of Kepler is equally true for every kind of orbit, 
including circular orbits ; but in the latter, the radius of the circle 
would be the radius-vector, and not only would the spaces described 
be equal, but also the different portions of the orbit, and consequently, 
the velocity would be uniform. The orbits of the satellites of Jupiter 
and Uranus are almost, if not exactly, circular. 

39. The squares of the periodic times of the planets are in 
proportion to the cubes of their mean distances from the 
sun, or central body. 

a. That is to say, if we square the times which any two planets 
require to complete a revolution around the sun, and then cube their 
mean distances, the ratio of the squares will be equal to that of the 
cubes. This law applies to the secondary as well as the primary 
planets. 

b. History. — This is the third and most celebrated of Kepler's laws. 
It establishes a most beautiful harmony in the Solar System. In his 
work on " Harmonics," Kepler first made it known, with a perfect 
burst of philosophic rapture. " What I prophesied, twenty-two years 
ago, — that for which I have devoted the best part of my life to astro- 
nomical contemplations, — at length I have brought to light, and have 

Questions. — a. Velocity of a planet — when variable ? b. When uniform ? 39. Re- 
lation of periodic times to distances ? a. Is it true of the satellites ? b. History of its 
discovery ? (Repeat the three laws of Kepler.) 






34. THE ORBITAL REVOLUTIONS 

recognized its truth beyond my most sanguine expectations. It is now 
eighteen months since I got the first glimpse of light, three months 
since the dawn ; very few days since the unveiled sun, most admirable 
to gaze on, burst out upon me. Nothing holds me ; I will indulge 
in my sacred fury. If you forgive me, I rejoice ; if you are angry, I 
can bear it. The die is cast, the book is written, — to be read either now 
or by posterity, I care not which : it may well wait a century for a 
reader, as God has waited six thousand years for an interpreter of his 
works." 

Sir John Herschel remarks of this law, " Of all the laws to which 
induction from pure observation has ever conducted man, this third 
law of Kepler may justly be regarded as the most remarkable, and the 
most pregnant with important consequences." 

c. Demonstration cf Kepler's Laws. — These laws were deduced 
by Kepler, as matters of fact, from the recorded observations of him- 
self and others ; but he failed to show the principle on which they are 
founded, and by which they are connected with each other. This was 
reserved for Newton, who, by the discovery and application of the law 
of gravitation, confirmed the truth of these laws by exact mathematical 
reasoning and calculation. 

d. Kepler's Third Law not quite true. — The third law is, how- 
ever, absolutely correct only when we consider the planets as mathe- 
matical points, without mass. Owing to the immense mass of the 
sun, this is relatively so nearly the fact, that the variation from the 
truth is very slight. 

40. The eccentricity of the large planets' orbits is very 
small, that of Mercury being the greatest, and Venus the 
least. The orbits of the Minor Planets are generally remark- 
able for their great eccentricity. 

a. Comparative Eccentricities. — The eccentricity of a planet's 
orbit is measured by comparing it with one-half of the major axis. 
The following is an approximate statement of the eccentricities of the 
large planets : — Mercury, | ; Mars, f ; Saturn, -fg- ; Jupiter, -fc ; Ura- 
nus, -£- 2 - ; Earth, -^ ; Neptune, rfr ; Venus, xis- The greatest of any 
of the minor planets is a little over ^. 

Questions. — c. By whom was their truth mathematically proved ? d. What modi- 
fication of Kepler's third law is required ? 40. What is the amount of eccentricity of 
the planets' orhits ? a. State their comparative eccentricities. 



OF THE PLANETS. 



35 



The annexed diagram will aid in giv- Fig. 23- 

ing the student a correct idea of the 
figure of the planets' orbits. This dia- 
gram represents an ellipse, the eccentri- 
city of which is |, or much greater than 
that of the most eccentric of the minor 
planets. It will be apparent, therefore, 
that the actual figure of the planets' or- 
bits is but slightly different from that of a 
circle. If drawn on paper, the eye could 
not detect the difference. 

41. The Mean Place of a 
planet is that in which it would 
be if it moved in a circle, and of 
course, with uniform velocity ; the tbtje place is that in 
which it is actually situated at any particular time. 

42. The angular distance of the true place from the mean 
place, measured from the sun as a centre, is called the Equa- 
tion of the Centre. 

Fig. 24. 



/ i 

F C F 



ELLIPSE — ECCENTEICITT, §. 




MEAN AND TKXTE PLACES OF A PLANET. 



In the above diagram, the ellipse represents the actual orbit of the planet, 

Qtjestiohs. — 41. What is mean place? True place? 42. Equation of the centre? 
Explain from the diasrram. 



■i 



36 THE ORBITAL REVOLUTIONS 

and the dotted circle the corresponding circular orbit. The points marked 
T represent the true places, and those marked M, the mean places of the 
planet. As the radius-vector passes over greater portions of the orbit in 
the perihelion than in the aphelion, the mean place is before or east of the 
true place, as the body moves from aphelion to perihelion, and behind or 
west of it in the other half of its revolution. The angle contained between 
the radius-vector and the radius of the circle is the equation of the centre. 

43. The planets do not all revolve around the sun in the 
same plane, but in planes slightly inclined to each other. 
The angle which the plane of a planet's orbit makes with 
that of the earth's orbit is called the Inclination of its 
Orbit. 

44. Of all the primary planets, Mercury has the greatest 
inclination of orbit (7°), and Uranus the least (46'). The 
Minor Planets are remarkable for a much greater inclination 
of their orbits than than that of the other planets. 

a. Since the planets' orbits are all inclined to that of the earth, each 
one must cross the plane of it in two points. These two points are 
called the Nodes j one the ascending node, and the other the descend- 
ing node. 



INCLINATION OF OBBITS. 

Fig. 25 represents an oblique view of the orbits of the earth and Venus. 
E is the ascending, and F, the descending node. E F the line of nodes, 
and A S G the angle of inclination of the orbit. 

Questions.— 43. What is meant by inclination of orbit t 44. Which planet has the 
greatest ? Which has the least ? Orbits of the Minor Planets— why remarkable ? 



OF THE PLANETS. 



37 



45. The Nodes* of a planet's orbit are the two opposite 
points at which it crosses the plane of the earth's orbit. 

46. The Ascending Node is that at which the planet 
crosses from south to north ; the Descending Node, that 
at which it crosses from north to south. The straight line 
which joins these points is called the Line of Nodes. 

Q is the sign of the ascending node ; 15 , of the descending node. 
Fig. 26. 




INCLINATION OF PLANETS' ORBITS. 

Fig. 26 represents the position of the plane of each orhit in relation to 
that of the earth. The small amount of deviation from one uniform plane 
will be at once apparent. These planets, however, on account of their vast 
distance from the sun, depart very far from the plane of the earth's orbit. 
Thus, Mars, although having only 2° of inclination, may be nearly 5 mil- 
lions of miles from this plane ; and Neptune, about 85 millions. 



From the Latin word nodus, meaning a knot. 



Questions.— 45. What are nodes? 
node ? Line of nodes ? 



3. What is the ascending node ? Descending 



CHAPTER V. 

DISTANCES, PEKIODIC TIMES, AND ROTATIONS OF THE 
PLANETS. 

47. The distances of the planets from the sun are so great 
that they can only be expressed in millions of miles. 

a. Idea of a Million. — A million is so vast a number that we can 
form no true conception of it without dividing it into portions. To 
count a million, at the rate of 5 per second, would require about 2£ 
days, counting without intermission, night and day. A railroad car, 
traveling at the rate of 30 miles per hour, night and day, would require 
nearly four years to pass over a million of miles. In stating the dis- 
tances of the planets, the rate of the express train may be employed as 
a standard of comparison, so that the pupil may obtain something 
more than merely a knowledge of figures in learning these almost 
inconceivable distances. 

48. The following are the mean distances of the planets 
from the sun, expressed in approximate round numbers : — 

Mercury, . 35 millions. Jupiter, . 476 millions. 

Venus, . 66 " Saturn, . 872 " 

Earth, . . 91 J " Uranus, . 1,754 " 

Mars, . . 139 " Neptune, 2,746 " 

Minor Planets, . . 260 millions (average). 
a. Illustration.— Multiply each of these numbers expressing mil- 
lions by four, and we shall find the time which an express train start- 
ing from the sun would require to reach each of the planets. In the 
case of the nearest planet, this period would be 140 years, and of the 
most remote, almost 11,000 years. A cannon ball moving at the rate 
of 500 miles an hour, would not reach Neptune in less than 626 years. 

Questions.— 47. Distances of planets — how expressed ? a. Idea of a million ? 48. State 
the mean distances of the primary planets from the sun. «. What illustration is given ? 



PERIODIC TIMES OF THE PLANETS. 39 

b. Body's Law. — A comparison of the distances given above will 
show a very curious numerical relation existing among them, each 
distance being nearly double that next inferior to it. A more exact 
statement of this numerical relation was published in 1772 by Profes- 
sor Bode, of Berlin, although not discovered by him : it has usually 
been designated " Bode's Law." Take the numbers 

0, 3, 6, 12, 24, 48, 96, 192, 384; 
each of which, excepting the second, is double the next preceding ; 
add to each 4, and we obtain 

4, 7, 10, 16, . 28, 52, 100, 196, 388; 
which numbers very nearly represent the relative proportion of the 
planets' distances, including the average distance of the Minor Planets. 
In the case of Neptune, the law very decidedly fails, and, conse- 
quently, has ceased to have the importance attributed to it previous 
to the discovery of this planet in 1846. 

PERIODIC TIMES OP THE PLANETS. 

49. The following are the periods of time occupied by the 
planets respectively in completing one revolution around 
the sun : — 



Mercury, . 88 days. 


Jupiter,* . 12 yrs. (nearly.) 


Venus, . 224J " 


Saturn, . 29^ " 


Earth, . . 365| " 


Uranus, . 84 « 


Mars, . . 1 yr. 322 days. 


Neptune, 165 " 



Thus the year of Neptune is about 700 times as long as that of 
Mercury. 

50. Of all the primary planets, Mercury moves in its orbit 
with the greatest velocity, and Neptune with the least ; the 
the velocities of the planets diminishing as their distances 
from the sun increase. 

a. This is in accordance with Kepler's third law ; since the ratio of 
the periodic times increases faster than that of the distances ; the square 

Questions.— ft. What is Bode's law? 49. State the periodic times of the primary 
planets. 50. Which planet moves with the greatest velocity? Which, the least? 
a. Why is this ? 



40 AXIAL KOTATIOKS OF THE PLANETS. 

of the former being equal to the cube of the latter. Thus, if the dis- 
tance of one planet is four times as great as that of another, the 
periodic time will not be simply four times as long, but eight times as 
long ; that is, the square root of the cube. {y~¥— j/64 = 8). Hence, 
as the planet has a longer time in proportion to the distance traveled, 
its velocity must be diminished. 

b. Comparative Velocities.— The following table exhibits the mean 
hourly motion of the primary planets in their orbits : — 

Mercury, . . 104,000 miles. Jupiter, . . 28,700 miles. 

Venus, . . 77,000 " Saturn, . . 21,000 " 

Earth, . . . 65,500 " Uranus, . . 15,000 " 

Mars, . . . 53,000 " Neptune, . . 12,000 " 

c. Illustration. — What an amazing subject for contemplation does 
this table present ! For example, the weight of the earth in tons is 
computed to be about 6,000,000,000,000,000,000,000 ; that is to say, six 
thousand million million times a million, or 6,000 X 1,000,000 X 1,000,- 
000 X 1,000,000. . Yet this body so inconceivably vast is rushing 
through the abyss of space with a velocity of 1,000 miles per minute, 
or about 15 miles during every pulsation of the heart. But the earth 
in comparison with the body around which it is revolving is as a single 
grain of wheat compared with four bushels. 

d. To find the Houiiy Motion. — This can be done by the applica- 
tion of very simple principles. The orbits being nearly circles, twice 
the mean distance will give us the diameter, and 3| times the diameter 
will give the circumference, or whole distance traveled in the periodic 
time. Then finding the number of hours in this time, and dividing the 
whole distance by this number, we obtain the hourly motion. Thus, 
Mercury's mean distance is 35 million miles ; then 35 X 2 X 3f = 220 
millions, the whole distance traveled in 88 days, or 88 X 24 = 2112 hours ; 
and 220 million -=- 2112 = 104,166 miles. 

AXIAL KOTATIONS OF THE PLANETS. 
51. Besides revolving around the sun, the planets revolve 
upon their axes in the same direction as they revolve in 
their orbits; that is, from west to east. (See Art. 18, a,) 
This is called their Diukkal Eotatiox 

Questions. — b. State the comparative velocities of the planets. c. Illustration ? 
d. How is the hourly motion in the orbit found ? 51. What is meant by diurnal 
rotation ? 



AXIAL ROTATIONS OF THE PLANETS. 41 

52. The Axis of a planet is the imaginary straight line 
passing through its centre, on which we conceive it to 
rotate. 

53. A planet must rotate with its axis either perpen- 
dicular or oblique to the plane of its orbit. The axes of the 
planets are all considerably oblique, excepting that of Jupi- 
ter, which is only 3° from the perpendicular ; that of Venus 
is supposed to be 75°. 

54. The angle which the axis of a planet makes with a 
perpendicular to its orbit, is called its Inclination of Axis. 

Fig. 27. 






INCLINATION OP JTTPITEB, EARTH, AND VENUS. 

a. The inclination of the axis of each planet, as far as it has been 
discovered, is as follows : — 



Mercury, . 


. (unknown.) 


Jupiter, . 


. 3°. 


Venus, 


. 75°. (?) 


Saturn, 


. 26f°. 


Earth, . . 


. 23i°. 


Uranus, •. 


. (unk 


Mars, . . 


. 28i°. 


Neptune, . 





b. How to Discover the Rotation. — The usual method of dis- 
covering the rotation of a planet is to examine the disc with a powerful 
telescope, so as to find, if possible, any spots upon it, and then to detect 
any regular movement of such spots across the disc. Let the pupil 
stand a short distance from a terrestrial globe, and let it be caused to 
revolve, and he will observe the marks upon it move across, and alter- 

Qtjebtions.— 52. What is the axis of a planet ? 53. Are the axes perpendicular, or 
ohlique? 54. What is inclination of axis? a. State the axial inclination of each 
planet, b. How is the axial rotation of a planet discovered ? 



42 



AXIAL ROTATIOKS OF THE PLANETS. 



nately disappear and re-appear. The same thing must, of course, occur 
in our observation of the planets, if they have a diurnal motion. 

55. The times of rotation of the planets respectively are 
as follows : 



Mercury, . 


. 24| hours. 


Jupiter, . 


. 10 hours. 


Venus, 


■ %H « 


Saturn, . 


. 10i " 


Earth, . . 


. 24 


Uranus, . 


. 9i " (?) 


Mars, . . 


.24i « 


Neptune, 


. (unknown.) 



a. It will be observed that the terrestrial planets all perform their 
rotations in about 24 hours ; but that the major planets require less 
than one-half that time. 

h. Sun's Rotation. — The sun also rotates upon an axis, but requires 
about 608 hours, or 25£ days to complete one rotation. The inclina- 
tion of its axis to the plane of the earth's orbit is about 7£°. 



Questions. — 55. State the time of the rotation of each planet, a. What distinction, 
in this respect, between major and terrestrial planets ? b. Does the sun rotate ? In 
what time ? 



CHAPTER VI. 

ASPECTS OF THE PLANETS. 

56. The Aspects of the planets are their apparent posi- 
tions with respect to the sun or to each other. The principal 
aspects, that is, those most frequently referred to, are Con- 
junction, Quadrature, and Opposition. 

57. A planet is said to be in Con junction with the sun 
when it is in the same part of the heavens. 

That is, if the sun is in 
the east, the planet must also 
be in the east, both being 
seen, if visible, precisely in 
the same direction. It is evi- 
dent that in the case of the 
inferior planets, this may oc- 
cur in two ways ; namely, 
when the planet is at that 
point of its orbit which is 
nearest to the earth or at the 
point most remote ; or, in 
other words, when the earth 
and planet are both on the 
same side of the sun, or on 
opposite sides. Of course a 
superior planet, to be in con- 
junction, must be on the oppo- aspects. 
site side of the sun from the earth. 

58. Conjunction may be Inferior or Superior. Inferior 



Fig. 28. 

8UPEKI0B CONJUNCTION 
, ©- ^. 



SUPERIOR 



0*\ 



INFERIOR 



7& 



OPPOSITION 



Questions.— 56. What is meant by aspects of the planets? 5T. When is a planet 
in conjunction ? 58. Of how many kinds ? What is inferior conjunction? Superior ? 



44 ASPECTS OF THE PLANETS. 

conjunction is that in which the planet is between the earth 
and the sun; superior conjunction is that in which the 
planet is on the opposite side of the sun from the earth. 

59. A planet is said to be in Opposition with the sun 
when it is in the opposite part of the heavens. 

a. That is, while the sun is in the east, the planet, if in opposition, 
must be in the west. If Jupiter, for example, should be rising just as 
the sun is setting, or vice versa, it would be in opposition. It is obvious 
that the superior planets only can be in opposition, and that when in 
that position, they are at the points of their orbits nearest to the earth. 

b. These different aspects obviously depend upon the angular, or 
apparent, distance of a planet from the sun. [See Introduction, Art. 
18, a]. In conjunction, there is no angular distance, unless we regard 
the difference in the planes of the orbits ; and when the planet is in 
conjunction and at either of the nodes, none whatever. In opposition, 
the angular distance is 180°. 

60. The angular distance of a planet from the sun is called 
its Elongation. 

61. A planet is said to be in Quadrature when its elon- 
gation is 90°. 

a. The position of quadrature in the heavens is half-way between con- 
junction and opposition, the planet being so situated that the straight 
lines that connect the earth with the sun and planet, respectively, make 
a right angle with each other. Thus if a planet were in quadrature, 
it would be in the south, or near it, either at sunset or sunrise, accord- 
ing as it were either east or west of the sun. It will be obvious, from 
Fig. 28, that, viewed from the earth as a centre, the position of quad- 
rature in the orbit is not half-way between conjunction and opposition, 
but much nearer the latter. 

b. There are, in all, five aspects of the planets, depending on their 
relative positions. The following are their names, the angular dis- 
tances, and the characters used to denote them : 

Questions. — 59. When is a planet in opposition ? a. Which planets can be in oppo- 
sition ? b. What is the angular distance of a planet in conjunction ? In opposition ? 
60. What is elongation ? 61. Quadrature ? a. Where is quadrature relatively to con- 
junction and opposition? b. Enumerate and define the five aspects, and write the sign 
of each. 



ASPECTS OF THE PLANET! 



45 



Conjunction, 


• 6 


0°. 


Trine, . . 


. A 


120°. 


Sextile, . . 


. * 


60°. 


Opposition, 


8 


180°. 


Quartile, . . 


. □ 


90°. 









Fig. 29. 




In the diagram, the graduated semicircle cuts the sides of all the angles 
which have their vertices at E, and serves to measure the angular distance 
of each planet from the sun. V and V" represent Venus in superior and 
inferior conjunction, the elongation being, at those points, 0° ; while at V, 
it is at its point of greatest elongation. It will be obvious from this dia- 
gram that no inferior planet can be 90° from the sun. M represents Mars 
in opposition, and M' the same planet in quadrature. The aspect of M and 
V or V" is opposition ; of M' and V or V', quartile. 

. 62. The time which elapses between two similar elonga- 
tions of a planet is called its Synodic * Period. 

a. Thus the interval between two successive conjunctions or oppo- 
sitions is the synodic period. The synodic period would be the true 
periodic time if the earth were at rest ; but the earth is moving in its 
orbit in the same direction as the planet, with a velocity less than that 



* From the Greek words 
pathway. 



meaning together, and odos, which means a 



Questions.— 62. What is the synodic period ? a. Why not the true period ? Illus- 
trate hy the diagram. How to calculate the synodic period of the inferior planets ? 
(Fig. 30.) Of the superior planets ? (Fig. 31.) 



46 



ASPECTS OF THE PLANETS. 




I 



SYNODIC PEEIOD. INFEEIOB PLANETS. 



of the inferior planets and greater than that of the superior. Hence, 
the synodic period of an inferior planet must always be greater than 
the periodic time, while that of the superior planets is generally less. 

The diagram represents Venus at V 1 
in inferior conjunction with the sun, the 
earth being at E 1 . Now conceive Venus 
to move around once, so as to return to 
V 1 ; the earth will then have gone over 
about HI of her orbit, and reached E 2 , 
and Venus will not overtake her until 
she reaches E 3 , passing her first position, 
and hence making one revolution, and 
the part E 1 E 3 besides, while Venus 
makes two revolutions, and of course a 
corresponding part of her orbit besides. 
This part of the orbit of each is about 
to of the whole, in the case of Venus. 
For since Venus completes a revolu- 
tion, or 860°, in 224| days, she moves 
about 1.6° per day; while the earth moves about .98° per day ; hence Venus 
gains .62° per day; but she has 360° to gain, as she leaves V, and 360° -4- 
.62° = 582 days. The true synodic period is 584 days. Now, 584 -*-224| = 
2.6, number of revolutions of Venus during one synodic period ; and 584 
-+- 365i = 1.6, number of revolutions of the earth ; and 2.6 rev. — 2 rev. == T ° 5 
rev.= E* E 3 or V» V 3 . 

The synodic periods of the superior plan- 
ets, are illustrated in the annexed diagram. 
Let J 1 represent Jupiter in opposition, the 
earth being at E 1 . As Jupiter's periodic 
time is about 12 years, when the earth, after 
performing a revolution, returns to E 1 , 
Jupiter has passed over T V of its orbit, and 
reached J a , and the earth moving a short 
distance farther overtakes it at J 3 . In this 
case, the superior planet only moves over 
a fraction of its orbit, while the earth moves 
over the same fraction of its orbit, and one 
whole revolution. We can find the synodic 
period of Jupiter from the true period, in 
synodic pebiod, suPEEioE planets. tne lowing manner :— As Jupiter, per- 
forms onlyrV of a revolution while the 
earth performs a whole one, the earth gains \\ of a revolution, while perform- 
ing one ; but to overtake Jupiter when starting from E 1 , after opposition, 



Fig. 31. 




ASPECTS OE THE PLANETS. 



47 



she has to gain an entire revolution, and 1-H£ = r?-. Now H of 365? days 
= 399 days (nearly) ; which is the synodic period of Jupiter. 

If the periodic time of any superior planet were exactly double that of 
the earth, its synodic period and periodic time would be equal. This is 
nearly true of Mars ; its periodic time being 1 yr. 322 days, and its synodic 
period, 2 yrs. 50 days. 

63. When a planet appears in the evening, just after sun- 
set, it is called an Evening Star ; when in the morning, just 
before sunrise, it is called a Morning Star. 

Um The inferior planets being always less than 90° from the sun, can 
only appear as morning or evening stars. Mercury being a small 
planet, and never having but a small amount of elongation, is a diffi- 
cult object to see ; Venus, being a large planet, and having a greater 
apparent distance from the sun, is a very brilliant and beautiful object, 
either as an evening or morning star. When the former, her elonga- 
tion must of course be east ; when the latter, west. The superior 
planets are morning or evening stars at different degrees of elongation, 
since they may be visible from sunset to sunrise. 

Fig. 32. 




VENT/8 AS MOBNING AND EVENING STAB. 

In the diagram, Fig. 32, Venus is represented as a morning and evening 



Questions. — 63. What is meant by morning star? By evening star? a. What is 
said of the inferior planets, in this respect ? Explain from the diagram. 



48 ASPECTS OF THE PLANETS. 

star. While Venus is on the side of the sun as represented at V, she must 
be an evening star, since, as the earth turns, any place at P must, as it 
turns from the sun at the time of sunset, still keep Venus in view by the 
angular distance contained between the lines drawn to the place from the 
sun and Venus respectively ; but when Venus is at V, the other side of the 
sun, the rotation of the earth would bring Venus into view at any place as 
P, before the sun. (The student should carefully notice the direction of 
the motion as indicated by the arrows.) Venus, of course, remains the 
same side of the sun during one-half of the synodic period, or 292 days. 

QUESTIONS FOE EXERCISE. 

1. When a planet is in quadrature, what is its elongation ? 

2. What is its elongation when in inferior conjunction ? 

3. What is its elongation in superior conjunction ? 

4. How many degrees of elongation has it when in opposition ? 

5. Which of the planets can be in inferior conjunction ? 

6. Which can be in superior conjunction ? 

7. Which can be in opposition ? 

8. Which can be in quadrature ? 

9. Can the elongation of Mercury or Venus exceed 90° ? 

10. Can that of Jupiter ? 

11. What is the greatest elongation of a superior planet ? 

12. When Venus is in inferior conjunction, and Mars in opposition, 
what is their angular distance from each other ? [See Fig. 29.] 

13. What is their angular distance when Venus is in inferior con- 
junction, and Mars in superior conjunction ? 

14. How many degrees are they apart when Venus is in superior 
conjunction and Mars is in quadrature ? 

15. When the elongation of Venus is 30°, and that of Mars is 120°, 
what is their angular distance from each other ? 

16. If Venus is 50° from Mars, and the latter body is in quadrature, 
what is the elongation of Venus ? 



CHAPTER VII. 

THE EARTH. 

64. That the earth is, in its general form, a spherical bodi? 
is plainly indicated by a few simple facts : 

1. Navigators are able to sail entirely around it either in 
an eastward or a westward direction ; 

& The earth and the sky always seem to meet in a circle, 
when the view is unobstructed ; 

3. The top of a distant object always appears above this 
circle, before the lower parts ; as the sails of a ship before 
its hull ; 

4- The elevation of the spectator causes this circle to sink, 
so as to show more of the earth's surface, and equally on 
all sides ; 

5. The apparent movements of the heavenly bodies 
around the earth, some in large circles, some in small circles ; 
one particular star in the heavens not appearing to have 
any motion at all. 

a. This last circumstance is accounted for by supposing that the 
earth's axis points to this star. Hence it is called the North, or Pole Star. 

b. The first practical proof that the earth is spherical was afforded 
by the voyage of Magellan, whose squadron, in 1519-22, sailed entirely 
around the earth. 

SECTION I. 

LATITUDE AND LONGITUDE. 

65. Points are located upon the surface of the earth by 
measuring their distances from certain established circles 

Questions. — 64. What five circumstances indicate that the general form of the earth 
is spherical ? a. What is the north star ? 65. How are points located on the earth's 
surface. 



50 



LATITUDE AND LONGITUDE. 



conceived to be drawn upon it. The position of these cir- 
cles is determined by their relation to two fixed points, 
called the Poles. 

66. The poles are the two extremities of the earth's axis, 
one being called the Noeth Pole, and the other the South 
Pole. 

a. As the earth turns on its axis from west to east, it causes all tlfe 
other heavenly bodies to seem to revolve around it from east to west, 
in circles contracting in size towards the fixed point of the heavens, 
called the celestial pole, near which is the pole-star. The celestial 
poles correspond to the poles of the earth, being the two points at which 
the earth's axis, if extended, would meet the sphere of the heavens. 

67. The great circle exactly midway between the two 
poles is called the Equatoe. Its plane divides the earth 
into northern and southern hemispheres. 

68. The great circles that pass through the poles are 
called meridian circles ; the half of a meridian circle that 

Fig. 33. extends from pole to pole, is called a Me- 

Mcridinns ridiml ' 

a. Meridian circles must, of course, be per- 
pendicular to the equator, and the plane of any 
one of them would divide the earth into eastern 
and western hemispheres. A great circle that 
is perpendicular to another is sometimes called 
a secondary to it. Thus the meridian circles 
are secondaries to the equator. 

69. The position of a place on the surface of the earth is 
indicated by its latitude and longitude. Latitude is dis- 
tance north or south from the equator ; Longitude, distance 
east or west from some established meridian, called a First, 
or Prime, Meridian. 




Qxtestions.— 66. What are the poles ? a. What are the celestial poles ? 67. What is 
the equator? 68. What are meridian circles ? Meridians? a.. Their relation to the 
equator ? What is a secondary ? 69. What is latitude ? Longitude ? 




LATITUDE AND LONGITUDE. 51 

70. Small circles parallel to the equa- 
tor are called Parallels or Latitude. 

71. Latitude is reckoned on a meridian, 
from the equator to the poles ; longitude 
is reckoned from the prime meridian 
round to the opposite meridian. 

a. Distance from any great circle must be 
reckoned on a secondary to that circle. It 
will be easily perceived by the pupil that the poles have the greatest 
possible latitude — namely, 90° ; and that places situated under the me- 
ridian opposite the prime meridian, have the greatest longitude, or 
180° east or west ; also, that a place situated at the intersection of the 
prime meridian with the equator can have neither longitude nor 
latitude. 

b. Difference of Time. — Difference of Longitude causes difference 
of time. Since the earth turns toward the east, any place east of 
another place, must have later time, because it is sooner carried, by the 
motion of the earth, under the sun ; and, as an entire rotation, or 360°, 
is performed in 24 hours, 15° of longitude must be equivalent to one 
hour of time. Thus, London is 74° east of New York ; and, conse- 
quently, when it is noon at New York, it is 5 o'clock in the afternoon 
at London, the sun having passed the meridian five hours earlier. 

c. Difference of Longitude may be converted into Difference 
of Time, by multiplying the degrees and minutes by 4 ; the former of 
which will then be minutes of time ; and the latter, seconds. For 
since -^ the number of degrees is equal to the number of hours, fif,or 
4 times, the degrees must be equal to the minutes ; and, for the same 
reason, 4 times the minutes of space must be equal to seconds of 
time. 

d. To convert Difference of Time into Difference of Longitude, 
reduce the hours to minutes, and divide by 4. For since 15 times the 
hours are equal to the degrees, -fo of 15, or \, the minutes must be 
equal to the degrees. 



Questions.— TO. What are parallels of latitude ? 71. How are latitude and longitude 
reckoned ? a. Where is the latitude greatest ? The longitude ? What point or place 
on the earth's surface has neither latitude nor longitude ? b. How does difference of 
longitude cause difference of time? e. How to convert difference of longitude into 
difference of time ? d. How to convert difference of time into difference of longitude. 



52 



LATITUDE AND LONGITUDE. 



PROBLEMS FOR THE GLOBE. 

Problem I. — To find the latitude and longitude of a 
place : Bring the given place to the graduated side of the 
brass meridian [the circle of brass that encompasses the 
globe], which is numbered from the equator to the poles : 
and the degree of the meridian, over the place will be the 
latitude ; and the degree of the equator, under the meridian, 
east or west of the prime meridian, will be the longitude. 

Verify the following by the globe : 

LAT. LONG. 

London, . . . 5H° N. ; 0°. 
Paris, . . . 49° N. ; 2i° E. 
Washington, . 39° N. ; 77° W. 
Cincinnati, . 39° N. ; 84^° W. 



LA.T. LONG. 

C. Good Hope, 34° S. ; 18±° E. 
Berlin, . . 52£° N. ; 13^° E. 
Madras, . . 13° N. ; 80° E. 
Santiago, . . 32£° S. ; 70|° W. 



Problem II. — The latitude and longitude of a place 
being given, to find the place : Find the degree of longitude 
on the equator, bring it to the brass meridian, and under 
the given degree of latitude, on the meridian, will be the 
place required. 

EXAMPLES. 



1. What place is in lat. 30° 

2. What place " " 42£' 



N., and long. 90° W. ? Ans. New Orleans. 
N., " 71° W.? Ans. Boston. 



3. What place 



40f° N., 



74° W. ? Ans. New York. 



Problem III. — To find the difference of latitude or lon- 
gitude between any two places : Find the latitude or longitude 
of both places ; if on the same side of the equator or merid- 
ian, subtract one from the other ; if on different sides, add 
them ; the result will be the answer required. 

EXAMPLES. 

Find the difference of latitude and longitude of 

1. London and Naples. Ans. Lat. 10^-°, long. 14^°. 

2. New York and San Francisco. Ans. Lat. 3°, long. 58^°. 

3. Stockholm and Rio Janeiro. Ans. Lat. 82°, long. 61°. 



LATITUDE AND LONGITUDE. 53 

Problem IV. — To find all the places that have the same 
latitude as any given place : Bring the given place to the 
brass meridian, and observe its latitude ; turn the globe 
round, and all places that pass under the same degree of the 
meridian will be those required. 

EXAMPLES. 

What places have the same, or nearly the same, latitude as 

1. Madrid? Ans. Minorca, Naples, Constantinople, Kokand, Salt 

Lake City, Pittsburgh, New York. 

2. Havana ? Ans. Muscat, Calcutta, Canton, C. St. Lucas, Mazatlan. 

Problem V. — To find the places that have the same longi- 
tude as any given place : Bring the given place to the grad- 
uated side of the brass meridian, and all places under the 
meridian will be those required. 

EXAMPLE 

What places have the same, or nearly the same, longitude as 
London ? Ans. Havre, Bordeaux, Valencia, Oran, Gulf of Guinea. 

Problem VI. — A time and place heing given, to find 
what o'clock it is at any other place : Bring the place at which 
the time is given to the brass meridian, set the index to the 
given time, and turn the globe till the other place comes to 
the meridian, and the index will point to the time required. 

Note. — If the place be east of the given place, turn the globe westward ; 
if west, turn it eastward. 

This problem can be performed without the globe by finding the differ- 
ence of longitude, as indicated in Art. 71, c, d. 

EXAMPLES. 

1. When it is noon at New York, what o'clock is it at London ? 

Ans. 5 o'clock P.M. (nearly). 

2. When it is 10 o'clock A.M. at St. Petersburg, what o'clock is it at 

the City of Mexico ? Ans. 1 hour 20 min. A.M. 

3. When it is 9 o'clock P.M. at Rome, what o'clock is it at San Fran- 

cisco? Ans. Noon. 



54 THE HORIZON, 

Problem VII. — To find the distancce between any two 

places : Lay the graduated edge of the quadrant over both 

places, so that the division marked may be on one of them ; 

and the number of degrees between them, reduced to miles, 

will be the distance required. 

Note. — If geographic miles are required, multiply the degrees by 60 ; if 
statute miles, by 691. 

EXAMPLES. 

Find the distance in geograp7iic and statute miles between 

1. North Cape and Cape Matapan. Ans. 2,100 geog. miles ; 2,418f 

statute miles. 

2. Rio Janeiro and Cape Farewell. Ans. 4,980 geog. miles ; 5,736| 

statute miles. 



SECTION II. 

THE HORIZON. 

72. The Horizon * of a place is the circle which sepa- 
rates the visible part of the heavens from the invisible. 

a. The surface of the earth appears, to a person standing upon it, 
like a great plane, extending equally on all sides, and limited by a cir- 
cle at which the earth and sky appear to meet. As the elevation of 
the spectator increases, the greater is the extent of surface embraced 
within this circle, and the more extensive the visible heavens as com- 
pared with the invisible. On the other hand, an eye situated exactly 
on the earth's surface sees but a point of it, but still beholds a circle 
bounding the visible heavens, the plane of which would touch the 
earth's surface at the exact point where the eye is located. This circle 
is called the Sensible or Visible Horizon ; and the depression of it, due 
to the elevation of the spectator, the Dip of the Horizon. The follow- 
ing definitions may therefore be given of each :• 

73. The Sensible Horizon is that circle of the celestial 



* From the Greek word horizo, meaning to bound. 

Questions. — 72. What is the horizon of a place ? a. General phenomena connected 
with the horizon ? 73. What is the sensible horizon ? 




THE HOBIZON. 



55 



sphere the plane of which touches the earth at the place of 

the spectator. 

a. By the Celestial Sphere is meant the concave sphere of the heavens, 
in which the heavenly bodies appear to be placed, the observer being 
at the centre within, and looking upward. 

74. The Dip of the Horizon is the depression of the 
sensible horizon caused by the elevation of the spectator, 
and bringing a circular portion of the earth's surface into 
view. 

In the diagram, let the small circle 
whose centre is E, represent the 
earth, the portion of the large circle 
V Z V a part of the celestial sphere, 
and P the point, or place, of the spec- 
tator. Then the tangent S P S will 
represent the plane of the sensible 
horizon, and S Z S the visible heavens. 
Conceive the observer to stand above 
the surface at H ; the tangents H V 
and H V will then, at their points of 
contact, D and D, limit the visible 
part of the earth's surface, and at 
their extremities, V and V, the visi- 
ble heavens. S V or S V will be, of course, the dip of the horizon. At the 
point P, the visible part of the heavens is less than the invisible ; but at so 
great an elevation as H P (represented as about 1,000 miles), the visible 
part would be much greater than the invisible, and a large part of the 
earth's surface, denoted by the arc D D, would come into view. The dip, 
however, at any attainable height is very small, and only an inconsiderable 
portion of the earth's surface can ever be seen. The line R R represents the 
plane of a great circle, which divides the celestial sphere into equal parts, 
passing through the centre of the earth, and situated at a distance from 
the plane of the sensible horizon equal to the semi-diameter of the earth, 
or nearly 4,000 miles. 

75. The great circle of the celestial sphere which is paral- 
lel to the sensible horizon, is called the Bational Horizon. 

Questions. — a. What is meant by the celestial sphere t 74 What is the dip of the 
horizon t Explain by the diagram. 75. What is the rational horizon ? 




SENSIBLE AND RATIONAL HOKIZON. 



56 THE HORIZON. 

It divides the earth and the celestial sphere into upper and 
lower hemispheres. 

The terms upper and lower, above and below, and the like, are only 
applicable to the horizon. The rational horizon is the real horizon ; 
it is the standard circle for referring the apparent positions of all the 
heavenly bodies. 

76. The poles of the horizon are called the Zenith and 
the Nadir. The zenith is the point directly overhead ; the 
nadir is the point opposite to the zenith, and directly under 
our feet. 

The one is the pole of the visible, or upper, hemisphere ; the other, 
the pole of the invisible, or lower. Each is, of course, 90° from the 
horizon. 

77. Great circles conceived to pass through the zenith and 
nadir are called Vertical Circles, or Verticals. 

a. Vertical circles, being perpendicular to the horizon, are secondaries 
to it. The position of a body in the celestial sphere is defined by its 
distance from the rational Jwrizon, and some selected vertical circle ; 
just as the position of a place on the earth's surface is determined by 
its latitude and longitude. The vertical selected for this purpose is 
that which the centre of the sun reaches and passes at noon. This 
circle, of course, passes through the north and south points of the 
horizon, and also through the celestial poles, its plane intersecting the 
earth so as to form a terrestrial meridian. It is therefore called the 
Meridian of the Place. 

78. The Meridian of a Place is the vertical circle 
which passes through the north and south points of the 
horizon of that place. It divides the celestial sphere into 
eastern and western hemispheres. 

a. When a body is on the meridian, it is said to culminate, because 
it is at that time at its greatest distance above the horizon during 
24 hours. 



Qttebtions.— 76. What are the zenith and the nadir? 77. What are vertical circles? 
a. How is the position of a hody in the celestial sphere defined ? 78. What is the me- 
ridian of a place ? a. When is a hody said to culminate ? 



THE HOEIZOX. 



57 



Fig. 36. 
Zenith 



79. The distance of a body above the horizon is called its 
Altitude. It is reckoned on a vertical circle, from the 
horizon to the zenith. 

At the horizon, therefore, the altitude is 0° ; at the zenith, 90°. 

80. The distance of a body east or west from the meridian 
is called its Azimuth. It is reckoned on the horizon. 

a. Prime Vertical ; Amplitude. — The altitude and azimuth of a 
body would be sufficient to define its position in the visible heavens ; 
but astronomers sometimes employ another vertical as a standard of 
reference, namely, that which passes through the east and west points 
of the horizon, cutting the meridian at right angles. This is called 
the Prime Vertical ; and the distance of a body from it, north or south, 
is call the Amplitude. These are, at 
present, but little used. By the am- 
plitude of the sun is generally meant 
the distance at which it rises from 
the east, or sets from the west point 
of the horizon. 

In the diagram-, let N E S TV repre- 
sent the rational horizon, the circle 
passing through N S, the meridian, and 
that passing through E W, the prime 
vertical ; then if A he the position of 
the sun at rising, A E will represent its 
amplitude, and A N, its azimuth ; the 
altitude being 0°. 

81. The Zestth Distance of a body is its distance from 
the zenith reckoned on a vertical circle. 

The zenith distance is the complement of the altitude, that is, the 
difference between it and 90°. 

82. The circles which the heavenly bodies may be con- 
ceived to describe during their apparent daily revolution 
around the earth, are called Oiecles of daily Motion. 




iNadir 



Qxtestions. — T9. What is altitude ? 80. Azimuth ? 
What is amplitude? 81. What is zenith distance 
motion ? 



a. What is the prime vertical ? 
82. What are circles o* daily 



58 



THE HORIZON. 



Fig. 37. 



Parallel Sphere 




Uadi* 



Fig. 38. 

Right Sphere 
^emtla. 



Sphere. 



Pole 



a. Positions of the Sphere. — The circles of 
daily motion are parallel, perpendicular, or ob- 
lique to the horizon, according to the place of the 
observer upon the surface of the earth. When 
standing exactly at either of the poles, he would 
have the celestial pole in the zenith, and the 
a*o? ~) circles of daily motion would be parallel to the 

horizon ; this position is called a Parallel Sphere. 
At the equator, the celestial poles would be in the 
horizon, and the circles of daily motion perpen- 
dicular to it ; this position is called a Right 
At any place between the equator and 
the pole, the circles would be oblique 
to the horizon, and the pole would be 
raised to an altitude equal to the lati- 
tude of the place ; this is called an 
Oblique Sphere. 

b. In a parallel sphere, one-half of all 
the circles of daily motion are wholly 
above the horizon, and the heavenly 
bodies do not appear to rise and set, 
but to move around in parallel circles 
contracting in size toward the zenith ; 
in a right sphere, all the circles are 
divided equally by the horizon, there 
being as much of each above as below it ; 
in an oblique sphere, some of the circles of 
daily motion are wholly above the horizon, 
others wholly below it, and all between 
these, divided unequally by it. All this 
will be rendered apparent by the accompa- 
nying diagrams. 

83. The circle of an oblique sphere 
in which the stars never set is called 
the Ciecle of Perpetual Appari- 




Pole 



JVadir 



Fig. 39. 



Ohlique Sphere 




Questions. — ft. What are the three positions of the sphere ? Define each. b. How 
are the circles of daily motion divided by the horizon in each? 83. What is the circle 
of perpetual apparition ? Of perpetual occupation ? 



PAEALLAX. 



59 



tion ; that in which they neyer rise, the Circle of Per- 
petual Occult ation. 

84. That part of a circle of daily motion which is above 
the horizon, and which a body describes from its rising to 
its setting, is called the Diurnal Arc ; the part below the 
horizon is called the Nocturnal Arc. 

In the diagram of the oblique sphere (Fig. 39), H H represents the ra- 
tional horizon, Z and N the zenith and nadir, P P the poles, E E'the equa- 
tor extended to the heavens, and the dotted lines, circles of daily motion. 
Then Z E will be the same number of degrees as the latitude, E H will be 
the altitude at which the equinoctial or equator intersects the meridian, 
and P H will be the altitude of the celestial pole. Now E P is equal to Z H, 
each being 90° ; hence, by subtracting Z P from each, we find E Z = P H ; 
that is, the altitude of the pole equal to the latitude. 



PARALLAX. 

85. The True Altitude of a body is the distance at 
which it wonld appear to be from the horizon, if it could be 
viewed from the centre of the earth. 

In the diagram let the Fig. 40. 

small circle represent the 
earth, having its centre at E ; 
A, B, and C, a body as seen at 
different altitudes from the 
place, P ; E H, the plane of 
the rational horizon ; P h, the 
plane of the sensible horizon, 
and E Z, the direction of the 
zenith. At A, the body being 
in the sensible horizon, its ap- 
parent altitude will be noth- 
ing ; but if viewed from E, it 
would appear to be above the 
horizon a distance equal to the 
angle mE H, or its equal m A h, 
since the difference in direction between the lines E H or Ph, and Em is the 
difference between the apparent and true altitude. At B, there is evidently 




Questions.— 84. Define diurnal arc, and nocturnal arc. Explain Fig. 
Is the true altitude of a body? 



39. 85. What 



60 PAKALLAX. 

a less difference of direction between the lines P n and E o, and when the 
body is at C, the centre of the earth, the place of the observer, and the po- 
sition of the body being all on the same straight line, the true is the same 
as the apparent altitude. It is evident that the apparent altitude is always 
less than the true altitude, except when the body is seen in the zenith, as at 
C ; and that there is the greatest difference when the body is in the horizon, 
as at A. 

86. The difference between the true and apparent altitude 
of a heavenly body is called its Pakallax. 

87. The parallax of a body is greatest when it is in the 
horizon, and diminishes towards the zenith, where it is 
nothing. The parallax of a body when in the horizon is 
called its Horizontal Parallax. 

In the preceding diagram, the angle m A h, or its equal P A E, is called 
the angle of parallax, o B n, or P B E, is the angle of parallax for the posi- 
tion B. The angular distance of the sensible and rational horizons is, of 
course, the horizontal parallax. 

a. The greater the distance of a body from the earth, the smaller is 
the angle of parallax. 

Fig. 41. Thus the horizon- 

p A^^B ^^-- c _^^— - tal parallax of a body 

( L^ ' H H, or P A E ; but at 

B, it is the smaller 
angle B E H, or P B E. The horizontal parallax of any body is really the 
angle subtended by the semi-diameter of the earth at the distance of the 
body ; and, of course, the greater the distance, the smaller the angle. 

b. The horizontal parallax of the moon is nearly 1° ; that of the 
sun, less than 9". In a subsequent chapter, it will be shown that 
by finding the parallax of a body, we can determine its distance from 
the earth. 

88. Since the apparent altitude of a body is less than the 
true altitude by the amount of parallax, the effect of paral- 
lax is said to be to diminish the altitude. The apparent 

Questions.— 86. What is parallax ? 8T. Where is it greatest ? What is horizontal 
parallax ? Explain Fig. 41. a. What relation between the distance of a body and its 
parallax ? Explain by the diagram, b. What is the horizontal parallax of the moon 
and sun ? 88. What is the effect of parallax ? 



KEFKACTION. 61 

altitude is therefore corrected by adding the amount of 
parallax due to the particular elevation and the distance of 
the body. 

a. Other corrections would also have to be made to obtain the exact 
altitude ; namely, for the dip of the horizon caused by the elevation of 
the spectator, and for the effect of the atmosphere upon the direction 
of the rays of light which pass through it. The latter of these is 
called Bef raction. 

REFRACTION. 

89. Kefbactiok, in astronomy, is the change of direction 
which the rays of light undergo in passing through the 
earth's atmosphere. 

a. It is a general fact that the rays of light when passing obliquely, 
from one medium into another of a different density, are turned from 
their course, and made to pass more obliquely, if the medium which 
they enter is rarer, and less obliquely, if it is denser than that which 
they leave. Thus, in passing from air into water, or from water into 
glass, the direction would be less oblique ; but in passing from water 
into air, more oblique. 

Suppose n m to represent the surface of water, Fig 42 . 

and S O a ray of light, entering the water at O. 
Instead of keeping on in the direction S O, it is 
bent toward the perpendicular A B, and thus 
passes less obliquely. 




b. Now, as the earth's atmosphere is not of 
uniform density, but grows more and more 
dense toward the surface of the earth, the 
rays of light which proceed from any body 

are constantly bent more and more toward a perpendicular direction ; 
and since we see an object in the direction in which the ray of light 
strikes the eye, the apparent altitude of the body will be increased. 

Questions.— fit. What other corrections required for true altitude? 89. What is 
refraction ? a. State the general law. Explain by the diagram, b. Why is the alti- 
tude increased by refraction ? Explain by the diagram. 



62 



KEFKACTION. 




Fig. 43. Suppose E to represent the 

earth, and A B C D, portions 
or strata of the atmosphere, of 
different densities, P, the place 
of observation. Suppose a ray 
of light from the star S, strike 
the atmosphere at a; on ac- 
count of refraction, instead of 
proceeding in the direction S 
A, it describes a 6, 6 c, and c P, 
reaching the spectator at P, 
and in the direction of c P ; so 
that the star a )pears in that 
direction at S', and is thus 
elevated above its true posi- 
tion at S. As the atmosphere 
does not consist of distinct strata, as represented, but diminishes uniformly 
in density from the surface of the earth, the broken line a b c P, is in real- 
ity a curve, and the line S' P, a tangent to it at the point P. 

90. The effect of refraction is greatest upon a body when 
it is in the horizon, and diminishes toward the zenith, where 
it is nothing. At the horizon, it amounts to about 33 
minutes. 

a. There is no refraction at the zenith, because at that point every 
ray of light strikes the atmosphere perpendicularly, and refraction only 
takes place when the direction of the rays is oblique ; at the horizon, 
they are more oblique than they can be at any point above it ; hence 
the refraction is greatest there. 

91. At the horizon, the amount of refraction is somewhat 
greater than the apparent diameter of the sun or moon ; and 
hence these bodies appear to be above the horizon when 
they are actually below it. 

a. The times of the rising of all the heavenly bodies are, therefore, 
accelerated, and those of their setting retarded, by refraction ; each 
one appears to be above the horizon before it has actually risen, and 
is seen above the horizon after it has actually set. 

Questions.— 90. What is the effect of refraction at the zenith and horizon ? Why ? 
91. What is the amount of refraction at the horizon ? a. Effect on the rising and set- 
ting of the heavenly bodies ? 



APPARENT MOTIONS OF THE SUN. 63 

b. Refraction very rapidly diminishes from the horizon towards the 
zenith. At the horizon its mean value is 33' ; at 10° of altitude, 15V J 
at 30°, H' ; at 45°, 57" ; at 80°, 10" ; at 90°, 0. 



SECTION III. 

APPARENT MOTIONS OF THE SUN AND STARS. 

92. The sun has two apparent motions around the earth ; 
namely, a diurnal motion from east to west, and an annual 
motion from west to east. The first is caused by the rota- 
tion of the earth on its axis, and the second, by its revolu- 
tion around the sun. 

a. The student should be careful to verify by his own observations 
the following statements respecting the sun's apparent motions : — 

1. Apparent Daily Motion.— The sun rises exactly at the east point 
of the horizon, and sets at the west point, twice a year ; namely, about 
the 20th of March and 23d of September ; and, on these days, it crosses 
the meridian at an altitude equal to the complement of the latitude ; 
that is, at the point where the celestial equator crosses the meridian. 

2. From March 20th to June 21st, the points at which the sun rises 
and sets move from the east and west toward the north, and its merid- 
ian altitude constantly increases ; from June 21st till Sept. 23rd, the 
points of rising and setting move back toward the east and west, and 
the meridian altitude diminishes ; from Sept. 23rd to Dec. 22nd, the 
points of rising and setting move toward the south, and the meridian 
altitude diminishes ; from Dec. 22nd to March 20th, the points of rising 
and setting move back toward the east and west, and the meridian alti- 
tude increases. There is thus a constant movement of the points of 
rising &nd- setting alternately from north to south, and a constant 
variation, up and down, of the point of culmination, except that the 
sun culminates at the same altitude for several days, about the 21st of 

Questions. — b. How fast does refraction diminish from the horizon? 92. What ap- 
parent motions has the sun ? How caused ? a. State the daily phenomena connected 
Tirith the apparent motions of the sun. What changes in the points of rising and set- 
ting ? In the point of culmination ? Solstices and equinoxes ? 



64 APPAKENT MOTIONS OF 

June and the 22nd of December. These two stationary points of cul- 
mination are called the Solstices* The points at which the culmina- 
tion of the sun coincides with that of the celestial equator are called 
the Equinoxes,\ because when the sun is at either of these points, the 
days and nights are exactly equal to each other. 

3. Apparent Annual Motion. — The sun appears to move toward 
the east among the stars ; for, if on any evening at sunset, or a short 
time after, we notice the distance of the sun from any star that may be 
visible, we shall find, in a few evenings, that this distance has grown 
less ; and hence, as the stars are fixed points, that the sun has moved 
toward the east. This motion will continue from month to month 
until the sun will be in conjunction with the star ; and then for six 
months the star will be no longer visible, but at the end of that time, 
will show itself above the eastern edge of the horizon just as the sun 
sets below the western ; and at the expiration of one year from the 
first observation, will have returned to the same relative position with 
the sun. In this way the sun appears to move from star to star toward 
the east, completing its circuit in 365^ days. 

93. The great circle of the celestial sphere in which the 
sun appears to revolve around the earth every year, is called 
the Ecliptic. 

The ecliptic may also be denned as the great circle of the celestial 
sphere in which it is intersected by the plane of the earth's orbit. Hence 
the plane of the ecliptic is the plane of the earth's orbit. 

94. The great circle of the celestial sphere exactly over 
the equator is called the Equinoctial, or Celestial 
Equator. 

The student must conceive these circles as marked out on the sky, 
the one crossing the other. (See diagram, Fig. 44.) 

95. Since the earth's axis is inclined to the plane of its 



* From the Latin words sol, meaning the sun, and sto, meaning to stand. 
t From the Latin words equus, meaning equal, and nox, meaning night. The 
arrival of the sun at either of these points produces equal days and nights. 

Questions.— State the phenomena connected with the sun's apparent annual motion. 
93. What is the ecliptic? 94. What is the equinoctial? 95. What is meant by the 
obliquity of the ecliptic ? Why is it 23 £° ? 



THE SUN AKD STARS. 



65 



orbit, or the plane of the ecliptic, making with it an angle 
of 23^°, the ecliptic and equinoctial must cross each other 
at an angle of 23 £°. This angle is called the Obliquity of 
the Ecliptic. 

Fig. 44. 
P OLE OF EC UP T , C 




P °LE OF ECLIPTIC 

ECLIPTIO AND EQUINOCTIAL. 

a. The obliquity of the ecliptic, and, of course, the inclination of the 
axis, are indicated by the difference between the highest and lowest 
daily culminating points of the sun, being equal to one-half of this dif- 
ference. For when it is at the equinoctial, it must c ulmin ate where 
the equinoctial crosses the meridian, that is, at an altitude equal to the 
complement of the latitude ; and when it is north or south of the equi- 



Qttestions.- 



How is the obliquity of the ecliptic indicated ? 



bb APPARENT MOTIONS OF 

noctial, it must culminate as far above or below the culminating point 
of the equinoctial. But this never exceeds 23^° either way ; hence, 
the obliquity or inclination must be 23|°. This departure of the sun 
from the equinoctial, as indicated by its daily motion, is called its 
Declination. 

b. To find the greatest and least meridian altitude of the sun at any 
place, the following rule may be given : Find the complement of the 
latitude, and to it add 23£° for the greatest altitude ; and from it sub- 
tract 23i° for the least. Thus for 
Fig. 45. New York the lat. of which is 

about 40r : 90° - 40 F = 49£° 
comp. of lat. Hence, 49F + 23£° 
= 73°, greatest altitude ; and49^° 
-23F = 26°, least altitude. 

In the diagram, P P represents 
the celestial poles, E E the equi- 
H noctial, Z N the zenith and nadir, 
H H the horizon, S the position. of 
the sun when 23|° north of the 
equinoctial, and S' its position 
when 23a° south of the equinoctial ; 
then E H will represent its alti- 
tude when at the equinoctial, E H 
+ E S, its greatest meridian alti- 




GEEATEST AND LEAST ALTITUDE OP THE SUN. 



tude ; and E H — E S, its least. 



96. The two opposite points of the ecliptic, where it 
crosses the equinoctial, are called the Equinoctial Points, 
or Equinoxes. The one which the sun passes in March is 
called the Vernal Equinox ; that which it passes in Septem- 
ber, the Autumnal Equinox. 

97. The two opposite points of the ecliptic at which the 
sun is farthest from the equinoctial, are called the Solstitial 
Points, or Solstices. The one north of the equinoctial is 
called the Summer Solstice ; the one south of it, the Winter 
Solstice. 



Questions—'*. How to find the greatest and least meridian "altitude of the sun? 
Explain by the diagram. 96. What are the equinoxes ? How distinguished ? 97. The 
solstices, and how distinguished ? 



THE SUN AND STARS. 67 

a. The equinoxes and solstices are sometimes called the cardinal 
points of the ecliptic ; they are 90° from each other, and, of course, 
divide the ecliptic into four equal parts. 

98. The Declination of a heavenly body is its distance, 
north or south, from the equinoctial. 

a. Declination corresponds to terrestrial latitude. At the equinoxes, 
the declination of the sun is 0° ; at the. solstices, it is 23^°, which is the 
greatest declination the sun can have. 

b. In a right sphere, the amplitude of the sun when it is rising or 
setting, is exactly equal to its declination. [Let the student verity this 
by an artificial globe.] 

99. Circles of Declination are great circles of the 
celestial sphere that pass through the poles, and are perpen- 
dicular to the equinoctial. 

a. Hour Circles. — Circles of declination correspond to meridian 
circles on the earth. When drawn at intervals of 15°, they are called 
Hour Circles, because the heavenly bodies, in their apparent diurnal 
revolution round the earth, pass from one to the other every hour ; 
since 360° + 24 = 15°. 

b. Hour Angle. — The angle included between the hour circle pass- 
ing through a body and the meridian of the place of observation is 
called the Hour Angle of the body. 

c. Oolures.— The circle of declination that passes through the equi- 
noctial points is called the Equinoctial Colure ; that which passes 
through the solstitial points is called the Solstitial Colure. 

d. The position of a heavenly body in the celestial sphere is defined 
by its distance from the equinoctial (or declination), and its distance 
from the equinoctial colure, reckoned eastward from 0° to 360°. The 
latter is called its Bight Ascension. 

100. The Eight Ascension of a heavenly body is its 
distance from the equinoctial colure, reckoned on the equi- 

Qxtestions.— a. What are these points sometimes called? 98. What is declination ? 
a. Greatest declination of the sun ? h. Amplitude of the sun in a right sphere — equal 
to what? 99. What are circles of declination? a. What are hour circles ? b. What 
is the hour angle ? c. What are colures ? d. How is the position of a body in the 
celestial sphere denned ? 100. What is right ascension ? 



68 



SIGNS OF THE ECLIPTIC 



noctial from the vernal equinox eastward entirely around 
the circle, that is, from 0° to 360°. 

a. Right ascension is frequently expressed in hours, minutes, and 
seconds ; reckoning, of course, 15° to an hour. (See Art. 71, b.) Thus, 
150° 30' 15" = 10 h 2 m 1«. 



SIGNS OF THE ECLIPTIC. 

101. The ecliptic is divided into twelve equal parts, called 
Signs. Each sign, therefore contains 30 degrees. 

102. The following are the names of the signs, the char- 
acters denoting them, and the day of the month on which 
the sun enters each (1867) : 



Spring 
Signs. 

Summer 
Signs. 

Autumn 



op 


March 20. 


b 


April 20. 


n 


May 21. 


25 


June 21. 


a 


July 23. 


m 


August 23. 


./\. 


September 23. 


n. 


October 23. 


t 


November 23. 


V? 


December 22. 


C£ 


January 20. 


X 


February 18. 



Vernal Equinox. 



Summer Solstice. 



Autumnal Equinox. 



Winter Solstice. 



Aries 

Taurus 

Gemini 
( Cancer 
■< Leo 
(Virgo 
( Libra 

< Scorpio 
( Sagittarius 

Winter ( Capricornus 

< Aquarius 
( Pisces 

a. The equinoctial points are, it will be observed, at the first degree 
of Aries and Libra ; and the solstitial points at the first degree of Can- 
cer and Capricorn. 

103. The Zodiac is a zone of the celestial sphere, extend- 
ing to the distance of eight degrees on each side of the 
ecliptic. 

a. The zodiac is therefore 16° wide : and within its limits are con- 

* ' 

Questions.— a. How is right ascension frequently expressed ? 101. How is the eclip- 
tic divided ? 102. Name the signs, and the day on which the sun enters each. a. At 
which of the signs are the equinoxes and solstices t Date of each ? 103. What is the 
zodiac ? a. "What is its width ? What does it contain ? 



PKECESSION. 69 

tained the orbits of all the planets, except some of the Minor Planets. 
It also contains twelve of the great groups of stars, called the Constel- 
lations of the Zodiac, which have the same names, and occupy nearly 
the same places, as the signs of the ecliptic. The names given to the 
signs are properly the names of the constellations : Aries, the ram ; 
Taurus, the lull; Gemini, the twins; Cancer, the crab ; Leo, the lion; 
Virgo, the virgin; Libra, the balance; Scorpio, the scorpion; Sagit- 
tarius, the archer ; Capricornus, the goat ; Aquarius, the water-carrier ; 
Pisces, the fishes. 

b. The places of the signs nearly corresponded with those of the 
constellations in the time of Hipparchus, by whom the constellations 
of the sphere were classified and arranged. He was the first to dis- 
cover (125 B. C.) the displacement of the signs, and to explain its 
cause, — the falling back (from east to west) of the equinoxes. This 
movement of the equinoctial points is called precession. 



PRECESSION. 

104. Peecession" is a gradual falling back of the equinoc- 
tial points from east to west. 

In other words, the sun, in his apparent annual revolution around 
the earth, does not cross the equinoctial always at the same points, 
but at every revolution crosses a little to the west of the points at 
which it crossed previously. The irregularity seems to exist in the 
motion of the sun ; but, of course, it is really in the motion of the 
earth. 

105. The amount of precession annually is about 50 
seconds (50.2") ; and consequently, to pass quite round the 
circle, the equinoxes require a period of nearly 26,000 years. 

a. For 360° X 60 x 60 = 1,296,000" + 50.2" = 25,816. 

b. In the time of Hipparchus, the vernal equinox was in the con- 
stellation Aries ; but it is now in Pisces, having fallen back about 28°. 
The signs and constellations corresponded about 185 B. C. 

Questions. — b. When did the signs of the ecliptic and the constellations of the zodiac 
correspond? 104. What is precession? Explain it. 105. What is the amount annu - 
ally ? a. Period required for a revolution ? b. In what constellation is the vernal equi- 
nox ? Where was it in the time of Hipparchus ? 



70 THE TEKKESTKIAL GLOBE. 

c. In maps of the heavens, and catalogues of the stars, the places of 
stars are marked by their declinations and right ascensions ; in some, 
however, they are indicated by their latitudes and longitudes, which 
terms, when applied to celestial objects, have a different meaning from 
that which they have as applied to places on the earth's surface. 

CELESTIAL LATITUDE AND LONGITUDE. 

106. The latitude or A heayekly bodt is its distance 
from the ecliptic, north or sonth. 

Celestial latitude must of course be reckoned upon a secondary to 
the ecliptic, from 0° to 90°. 

107. The longitude of a heatedly body is its dis- 
tance from a secondary to the ecliptic which passes through 
the vernal equinox, or first degree of Aries. It is reckoned 
from the vernal equinox eastward from 0° to 360°. 

a. Of course, neither the longitude nor right ascension of a body 
can be quite equal to 360° ; since that would bring it back to the point 
of commencement, or 0° ; it may, however, be any distance less than 
that ; as, 359° 59' 59". 

PROBLEMS FOR THE TERRESTRIAL GLOBE. 

Problem I. — To find the sun's longitude for any given 
day : Look for the given day of the month on the wooden 
horizon, and the sign and degree corresponding to it, in the 
circle of signs, will be the sun's place in the ecliptic ; find 
this place on the ecliptic, and the number of degrees between 
it and the first point of Aries, counting toward the east, 
will be the sun's longitude. 

EXAMPLES. 

1. What is the longitude of the sun June 21st 1 Ans. 90°. 

2. What is it February 22d ? Ans. 3371° 

3. What is it May 10th ? Ans. 50°. 

Questions.— c. Places of stars— how marked on maps ? 106. What is celestial lati- 
tude ? How reckoned ? 107. What is celestial longitude ? How reckoned ? a. Can 
the longitude be 360 6 f 



THE TEKKESTRIAL GLOBE. 71 

Problem II. — To find the right ascension of the sun: 
Bring the sun's place in the ecliptic to the edge of the brass 
meridian ; and the degree of the equinoctial oyer it, reck- 
oning from the first degree of Aries, toward the east, will be 
the right ascension. 

EXAMPLES. 

1. What is the right ascension of the sun October 18th ? Ans. 203£°. 

2. What is it May 2d ? Ans. 42°. 

Problem III — To find the declination of the sun: Bring 
the sun's place in the ecliptic to the edge of the brass merid- 
ian; and the degree of the meridian oyer it, reckoning 
from the equator, will be the declination. The declination 
may also be found by bringing the giyen day of the month 
as marked on the analemma to the meridian. 

EXAMPLES. 

1. What is the declination of the sun June 21st ? Ans. 23£° N. 

2. What is its declination Jan. 27th ? Ans. 18i° S. 

3. What is it April 16th ? Ans. 10° N. 

Problem IV. — To find what places have a vertical sun on 
any day in the year : Find the sun's declination, and note the 
degree on the brass meridian ; then turn the globe around, 
and all places that pass under that degree will be those 
required. 

EXAMPLES 

1. What places have a vertical sun March 20th ? Ans. All places 

under the Equator. 

2. To what places is the sun vertical December 22d? Ans. To all 

places under the Tropic of Capricorn. 

3. To what places is the sun vertical May 1st ? An,s. To all in lati- 

tude 16° N. 

Problem V. — To find the meridian altitude of the sun 
for any day of the year, at anyplace : Make the eleyation of 
the north or south pole above the wooden horizon equal to 



72 THE TERRESTRIAL GLOBE. 

the latitude, so that the wooden horizon may represent the 
horizon of that place ; bring the sun's place in the ecliptic 
to the brass meridian, and the number of degrees on the 
meridian from the horizon to the sun's place will be the 
meridian altitude. 

EXAMPLES. 

1. Find the sun's meridian altitude at New York, June 21st. Arts. 73°. 

2. At London, Jan. 27th. Ans. 20 s . 

3. Rio de Janeiro, September 23d. Ans. 67°. 

Problem VI. — To find the amplitude of the sun at any 
place, and for any day in the year : Proceed as in Problem V. ; 
then bring the sun's place to the eastern or western edge of 
the horizon, and the number of degrees on the horizon from 
the east or west point will be the amplitude. 

EXAMPLES. 

1. Find the sun's amplitude at London, June 21st. Ans. 39|° N. 

2. At Quito, September 23d. Ans. 0°. 

3. At Philadelphia, July 16th. Ans. 28° N. 

Problem VII. — To find the sun's altitude and azimuth at 
any place, for any day in the year, and any hour of the day : 
Proceed as in Problem V. ; then set the index to twelve, and 
turn the globe eastward or westward, according as the time 
is before or after noon, until the index points to the given hour. 
Then, for a vertical, screw the quadrant of altitude over the 
zenith, and bring its graduated edge to the sun's place in the 
ecliptic ; the number of degrees on the quadrant from the 
sun's place to the horizon will be the altitude, and the num- 
ber of degrees on the horizon, from the meridian to the 
edge of the quadrant, will be the azimuth. 

EXAMPLES. 

1. Find the sun's altitude and azimuth at New York, May 10th, 9 
o'clock A. M. Ans. Altitude, 45£° ; azimuth, 72^° E. 



DAY AND NIGHT. 



73 



2. At London, May 1st, 10 o'clock A. M. Ans. Altitude, 47°; azi- 

muth, 44° E. 

3. At London, March 20th, 3i o'clock P. M. Ans. Altitude 22° ; azi- 

muth, 59° W. 



SECTION IV. 



DAY AND NIGHT. 

108. The succession of day and night is caused by the 
rotation of the earth on its axis. 

As the earth turns on its axis, every place is brought alternately 
into the light and into the shade. All places turned toward the sun, 
so that its rays can shine upon them, have day ; and those turned 
away have night, because they are in the earth's shadow. 

109. The comparative length of day and night at any par- 
ticular place and time depends upon the sun's declination, 
or distance from the equinoctial. When the sun is north of 
the equinoctial, all places in the northern hemisphere have 
longer day than night, and those in the southern hemisphere, 
longer night than day ; but when the sun is south of the 



equinoctial, this is reversed. 

In the diagram, let H H represent the 
horizon, P P' the axis of the celestial 
sphere, E E' the equinoctial ; let also S 
be the sun in north declination, and S' 
in south declination ; it will be obvious 
that as the earth turns, the sun at S will 
appear to move in a diurnal arc, as a S 5, 
greater than the nocturnal arc a c b ; and 
at S', the diurnal arc mS'» will be less 
than the nocturnal arc mo n; while at E, 
in the equinox, the circle of daily motion 
described by the sun will be divided 
equally by the horizon. 



Fig. 46. 




LONGEST DAY AND NIGHT, 



Questions.— 108. What causes the succession of day and night ? 109. On what does 
the length of day and night depend ? How does the day compare with the night when 
the sun is north of the equinoctial ? When south of it ? Explain by the diagram. 



74 DAY AND NIGHT. 

110. All places under the equator have equal days and 
nights during the whole year. 

a. This will be obvious, if it is remembered that in a right sphere, 
all the circles of daily motion are perpendicular to the horizon, and 
equally divided by it ; so that whatever the declination of the sun 
may be, its diurnal arc must always be equal to its nocturnal arc. 

b. One half of the year, to places under the equator, the sun is in 
the north when on the meridian, and the other half in the south ; 
while on the 20th of March and the 23d of September, it is exactly 
overhead, or vertical. 

c. Since the sun's declination is never greater than 23£°, no place 
whose latitude, either north or south, is beyond that limit, can have a 
vertical sun ; and all places within these limits must have a vertical 
sun twice every year ; that is, as the sun moves north and on its return. 

111. The small circles parallel to the equator or equinoc- 
tial, at the limit of the sun's declination, are called the 
Tropics ; that at the northern solstice is called the Tropic 
of Cancer ; that at the southern, the Tropic op Capri- 
corn. 

a. Tropic means turning ; and these circles are called tropics, because, 
when the sun arrives at oDe, it turns back and goes to the other. They 
serve to bound that zone of the earth's surface within which the sun 
can be vertical. 

112. Places situated at either of the poles have constant 
day during the whole six months the sun is in the same 
hemisphere ; and constant night during the six months it is 
in the other. 

a. For in a parallel sphere, the equinoctial coincides with the hori- 
zon, and therefore, when the sun is north of the equinoctial, it must 
be above the horizon, and when south of the equinoctial, below it. 

b. Since the altitude of the pole is equal to the latitude, (Art, 82, a.) 

Questions.— 110. Day and night at places under the equator? a. Why? 6. When 
is the sun vertical? c. What places can have a vertical sun? 111. What are the 
tropics? How named? a. What does tropic mean ? 112. What places have constant 
day, and when ? a. Why ? b. How often does the sun cross the meridian at these 
places ? Explain by the diagram (Fig. 47), 



DAY AND NIGHT, 



75 



the distance of the circle of perpetual apparition from the equator 
is equal to the complement of the latitude ; and when the sun is 
within this circle, there must be constant day ; the sun keeping above 
the horizon, and crossing the meridian twice during the twenty-four 
hours,— once when it culminates, in the south or north, according as 
the place is in north or south latitude, and once at the opposite part of 
the circle. 

Suppose Z to be the zenith Fig. 47- 

of a place 15° from the north 2 p 

pole, and consequently in 75° 
N. latitude ; H IP being the 
plane of tbe horizon, P P the 
celestial poles, E E the plane 
of the equinoctial, S the sum- 
mer solstice, and "W the 
winter solstice : then PH' = 
75°, and a IP is the circle of 
perpetual apparition, and H & 
the circle of perpetual occul- 
tation. At d the sun has 15° 
of north declination, and at 
its point of culmination, a, 
crosses the meridian at an al- 
titude of 30° (H E + E a) ; 
while at the opposite point it 
just touches the horizon at IP; 
IP is obviously the north, because it is toward the pole. Going north from d 
toward the solstice S, and back from S to c, it is evident that the sun will be 
within the circle of perpetual apparition, and hence, there will be constant 
day ; while from c to e, the equinox, and from e to w, the circle of perpetual 
occultation, it will rise and set, its meridian altitude growing less and less 
until at n, it will appear at the horizon for a short time at noon each day, 
and finally disappear, remaining below the horizon while oroing south from 
n to W, the winter solstice, and north from W to m, where it again crosses 
the eircle of perpetual occultation, and then appears once more above the 
horizon. There is, therefore, constant day while it is passing over d Sc, and 
constant night while passing over n W m. 

c. Since the smallest circle of perpetual apparition or of perpetual 
occultation reached by the sun extends 66 \° from the pole, no place 
situated within 66^° from the equator, can have constant day, or day 




CONSTANT DAT AND NIGHT. 



Qttestions. — c. What is the limit of constant day and night? 



76 



DAT AND NIGHT 




S.Pole 

POLAB CIRCLES. 



of more than 24 hours' duration. Hence, the limit of constant day is 
the small circle round each pole, 23£° from it. These two parallels 
are called 'polar circles. 

113. The polar circles are two 
small circles, parallel to the equa- 
tor or equinoctial, and 23^° from 
the poles. The one round the north 
pole is called the Arctic Circle ; 
the one round the south pole, the 
Antarctic Circle. 

114. All places within the polar 
circles have constant day and con- 
stant night during a portion of 
each year; the duration of each 

being greater or less according as the place is nearer to the 
pole or farther from it. 

The polar circles serve to mark the limit of constant day and night. 

115. When the sun is in 
either of the solstices, all 
places in the same hemi- 
sphere with it have their 
longest day and shortest 
night, and those in the 
other, their shortest day and 
longest night. When it is 
in either of the equinoxes, 
the days and nights are of 

equal length in all parts of the earth, except at, or very near, 

the poles. 

116. The atmosphere of the earth increases the length 

of the day, both by refracting and by reflecting the sun's rays. 

Questions —113. What are the polar circles ? How named? 114. What places have 
constant day or night? 115. What is said of the day and night when the sun enters 
either solstice ? Either equinox ? 116. How is the length of the day increased ? 




EARTH AT THE SOLSTICE. 



TWILIGHT. 



77 



a. When the sun is in either 
of the equinoxes, one half of it 
would constantly appear above the 
horizon of a place at either of the 
poles, except for refraction, the 
effect of which is very great at 
those points ; so that the sun, at 
the equinox, appears wholly above 
the horizon, thus causing constant 
day, within one or two degrees of 
each pole. The general effect of eaeth at the equinox 

refraction is to increase the length of the day from six to ten minutes. 




TWILIGHT. 

117. When the sun is a short distance below the horizon, 
its rays fall on the upper portions of the atmosphere, which 
like a mirror reflect them upon the earth, and thus produce 
that faint light called twilight The morning twilight is 
generally called the dawn. 

Fig. 51. 
H' 




Let ABC represent three places on the earth, and A H", B IF, C H, their 
horizons respectively. Suppose S to represent the sun, a little below the 
horizon, its rays passing through the atmosphere in S C H" ; at A, no por- 
tion of the visible atmosphere is illuminated, and consequently there is no 
twilight ; at B, the part H" g H is illuminated, and at C, H"CH; twilight 
is produced at each of these points. 

" When the sun is above the horizon, it illuminates the atmosphere 
and clouds, and these again disperse and scatter a portion of its light 



Questions. — a. Effect of refraction? 117. What is twilight, and how produced? 
Explain by the diagram. Remark of Sir John Herschel. 



78 TWILIGHT. 

in all directions, so as to send some of its rays to every exposed point 
from every point of the sky. The generally diffused light, therefore,, 
which we enjoy in the day-time, is a phenomenon originating in the 
very same causes as twilight. Were it not for the reflective and scat- 
tering power of the atmosphere, no object would be visible to us out 
of direct sunshine ; every shadow of a passing cloud would be pitchy 
darkness ; the stars would be visible all day, and every apartment into 
which the sun had not direct admission would be involved in noc- 
turnal obscurity." — Sir John Herschel. 

118. The duration of twilight varies greatly at different 
parts of the earth; it is shortest at the equator, and 
increases toward the poles ; near the polar circles and within 
them, there is constant twilight during a part of each year. 

a. At the equator, the duration is lh. 12m. ; at the poles, there are 
two twilights during the year, each lasting about 50 days. This long 
twilight diminishes very much the time of total darkness at the poles ; 
for the sun is below the horizon six months, equal to 180 days, and 
deducting 100 days of twilight, there remain only 80 days, or less than 
three months, of actual night. 

119. Twilight does not cease until the sun is about 18° 
below the horizon. 

a. This is the generally received estimate, but there is considerable 
uncertainty about it. Some have found it to be as great as 24° ; others 
have reduced it to 16°. There is also a variation in different latitudes ; 
18° is the mean value. 

b. If the earth's atmosphere were more extensive than it is, the 
twilight would of course be longer, since the sun would not cease to 
illuminate the higher portions of the atmosphere until more than 18 s 
below the horizon ; and if the atmosphere were less extensive, the 
reverse of this would be the case. Knowing therefore the depression 
of the sun (18°) requisite for the cessation of twilight, we can calcu- 
late the extent or height of the atmosphere. Thus computed, it is 
about 40 miles. 

Questions. — 118. What is the duration of twilight at different places ? Where is there 
constant twilight? a. Duration of twilight at the equator? At the poles? 119. 
When does twilight cease ? «. Diversities of estimate ? b. What can we find by know- 
ing this fact ? c. Why is the duration of twilight different at different places ? Explain 
by the diagram (Fig. 52). 



PROBLEMS FOR THE GLOBE. 



79 



c. If the circles of daily motion were at all places equally inclined 
to the horizon, the duration of twilight would everywhere be the same ; 
since the earth would always have to turn the same amount to bring 
the sun 18° degrees below the horizon ; but the more oblique the circles 
are, the farther the earth has to turn, and hence the twilight is longer 
the nearer we go to the poles. 

Let the large circle repre- ^S* 52< 

sent the celestial sphere, e the P 

earth in the centre ; P H the 
altitude of the pole in one po- 
sition of the sphere, and P' H 
its altitude in one less oblique; 
E E and E' E' the equinoctial 
in each, and, of course, the 
direction of the circles of 
daily motion. In the more 
oblique sphere, that is,, at 
the place in the more north- 
ern latitude, the celestial 
sphere, or which is the same 
thing, the earth, would have 
to turn a distance on the 
diurnal circle, equal to e a, 
to bring the sun 18° below 

the horizon; while in the other position, the sun would reach the 
same point of depression when the sphere had turned only e b. Thus we 
see the nearer the perpendicular the diurnal circles are, the shorter the 
twilight ; while the more oblique they are, the longer the twilight. 

PROBLEMS FOR THE TERRESTRIAL GLOBE. 
Problem I. — To find on what two days of the year the 
sun is vertical at any place in the Torrid Zone : Turn the 
globe around, and observe what two points of the ecliptic 
pass under the degree of the brass meridian corresponding 
to the latitude of the place ; and the days opposite these 
points in the circle of signs will be those required. 

EXAMPLES. 

On what two days of the year is the sun vertical at 

1. Bombay ? Ans. May 15th and July 29th. 

2. Bahia ? Ans. Oct. 28th and Feb. 14th. 




DOTATION OF TWILIGHT. 



80 PROBLEMS FOR THE GLOBE. 

Problem II. — To find the time of the sun's rising and 
setting, and the length of the day, at any place, and on any 
day in the year : Elevate the pole as many degrees as are 
equal to the latitude of the place, find the sun's place, bring 
it to the meridian, and set the index to twelve. Then turn 
the globe till the sun's place is brought to the eastern edge 
of the horizon, and the index will show the time of the 
sun's rising ; bring it to the western edge, and the index 
will show the time of the sun's setting. Double the time 
of its setting will be the length of the day ; and double the 
time of its rising, the length of the night. 

Note. — The globe, of course, only shows this approximatively. A cor- 
rection would also be required for refraction. 

EXAMPLES. 

At what time does the sun rise and set, and what is the length of the 
day and night, 

1. At London, July 17th, ? Ans. Sun rises at 4, and sets at 8 ; length 

of day, 16 hours ; night, 8 hours. 

2. At New York, May 25th ? Ans. Sun rises at 4f , and sets at 7{ ; 

length of day, 14£ hours ; night, 9£ hours. 

Problem III. — To find the length of the longest and 
shortest days and nights at any place not within either of 
the polar circles : Find, by the preceding problem, the length 
of the day and night at the time of the northern solstice, 
if the place be north of the equator, and at the time of the 
southern solstice, if it be south of the equator ; and this 
will be the longest day and shortest night. The longest 
day is equal to the longest night, and the shortest day to 
the shortest night. 

EXAMPLES. 

What is the length of the longest and the shortest day 

1. At New York: ? Ans. Longest day, 14 hours 56 min. ; shortest 

day, 9 hours 4 min. 

2. At Berlin ? Ans. Longest, 16£ hours ; shortest 7£ hours. 



PROBLEMS FOR THE GLOBE. 81 

Problem IV. — To find the beginning, end, and duration 
of constant day at any place within either of the polar circles : 
Take a degree of declination on the brass meridian equal 
to the polar distance of the place, then on turning the globe 
around, the two points on the ecliptic which pass under that 
degree will be the places of the sun at the beginning and 
end of constant day. Find the day of the month corre- 
sponding to each, and it will be the times required. The in- 
terval between these dates will be the duration of constant 
day. 

Constant night is equal to constant day at a place situated under the cor- 
responding parallel in the other hemisphere. Hence, to find the duration 
of constant night at a place in north latitude, find the length of constant 
day at a place having the same number of degrees of south latitude. 

EXAMPLES. 

Find the beginning, end, and duration of constant day and night at 

1. North Cape. Ans. Constant day begins May 14th, ends July 

20th ; duration, 77 days. Constant night begins 
November 25th, ends January 27th ; duration, 73 
days. 

2. North Pole. Ans. Constant day begins March 20th, ends Sep- 

tember 23d ; duration, 187 days. Constant night 
begins September 23d. ends March 20th ; dura- 
tion, 178 days. 

Problem V. — To find the duration of tiuilight at any place 
not within either of the polar circles : Elevate the pole equal to 
the latitude, find the sun's place, bring it to the western edge 
of the horizon, and note the time shown by the index. Then 
screw the quadrant over the place, and bring its graduated 
edge to the sun's place ; turn the globe till the sun's place 
is shown by the quadrant to be 18° below the horizon, and 
the time passed over by the index will be the duration of 
twilight. 



82 THE SEASONS. 



EXAMPLES 



1. What is the duration of twilight at London, September 23d ? 

Ans. 2 hours. 

2. What is it at Dresden, April 19th? Ans. 2 hours 15 minutes. 



SECTION V. 

THE SEASONS. 

120. The Seasons are the four nearly equal divisions of 
the year, which are distinguished from one another by the 
comparative length of the day and night, and the difference 
in the amount of heat received from the sun. 

121. The causes of the seasons are the inclination of 
the axis of the earth to the plane of its orbit, and its revo- 
lution around the sun ; and the vicissitudes are regular, that 
is, always the same from year to year, because the axis 
always points in the same direction, or remains parallel to 
itself. 

. a. These four periods, called Spring, Summer, Autumn, and Winter, 
are marked and limited by the arrival of the sun at the vernal equi- 
nox, northern solstice, autumnal equinox, and southern solstice, respect- 
ively. The following statements will be understood by an inspection 
of the accompanying illustration (Fig. 53) : 

1. Sun in the Northern Solstice. — When the sun enters Cancer 
(northern solstice), the north pole is presented to the sun ; and summer 
is produced in the northern hemisphere, because the rays of the sun 
fall directly upon that part of the earth ; while winter occurs in the 
southern hemisphere, because there the sun's rays are oblique ; 

2. Sun in the Southern Solstice. — When the sun enters Capricorn 
(southern solstice), the south pole is presented to the sun, and summer 
occurs in the southern hemisphere, and winter in the northern ; 

Questions.— 120. What are the seasons ? 121. How caused ? a. How limited ? 
What are the seasons when the sun enters Cancer ? When the sun enters Capricorn ? 



THE SEASONS. 
Fig. 53. 



83 




THE SEASONS. 



3. Sun in the Equinoxes. — When the sun enters either of the equi- 
noxes, the earth's axis leans sidewise to it, and the rays are direct to 
the equator, and equally oblique on both sides of it. Consequently, 
there is neither summer nor winter ; but spring in that hemisphere 
which the sun is entering, and autumn in that which it has left ; 

4. Hence, when the sun enters Aries (vernal equinox), there is spring 

Questions.— When it is at either of the equinoxes ? When it enters Aries ? Libra ? 



84 



THE SEASONS. 



in the northern hemisphere, and autumn in the southern ; and when 
it enters Libra (autumnal equinox), the reverse is the case. 

&. By the sun's entering a sign, is meant its appearing at the first 
point of that sign in the ecliptic ; the earth, as seen from the sun, 
would appear, of course, at the first point of the opposite sign. 

In the inner circle of the diagram (Fig. 53), containing the names of the 
months, the dates give the times at which the earth enters the correspond- 
ing signs in the outer circle. Of course, the sun, at these dates, enters the 
opposite signs. 

122. Summer is caused by the rays of the sun being more 
nearly perpendicular than in the other seasons, so that the 
same part of the earth's surface receives a greater quantity 
of light and heat. Winter is caused by the greater obliquity 
of the sun's rays, in consequence of which the same quan- 
tity of light and heat is diffused over a greater surface. 

Fig. 54. 




SUMMEB AND WINTEE EATS. 



In Fig. 54, it will be observed that the same quantity of rays that covers 
the north polar circle, when they are direct, covers the whole space from 
the antarctic circle to the equator, when they are oblique. 

123. The seasons are not precisely of equal length, be- 
cause the earth revolves in an elliptical orbit, and conse- 
quently passes through one half of it in less time than the 
other. 

«. The perihelion of the orbit is in the 11th degree of Cancer, its 
Longitude being 100° 21' ; so that when the earth is at this point, the 



Questions.— b. What is meant by the sun' s entering a sign ? 122. How is summer 
caused? Winter? Explain by the diagram. 123. Are the seasons of equal length? 
a. Explain the cause. 



THE SEASONS. 



85 



Fig. 55. 



^TUMN/EQUJNOX 



sun is in the 11th degree of Capricorn, January 1st. Thus, the earth 
passes its perihelion, and is, consequently, nearest to the sun, in winter ; 
and the time occupied by the sun in going from Libra to Aries, that is, 
from the beginning of autumn to the beginning of spring, is shorter by 
about eight days than the time from Aries to Libra, or from spring to 
autumn again. The seasons are, of course, reversed in the southern 
hemisphere. 

b. The duration 
of the seasons, re- 
spectively, is as fol- 
lows : Spring, 92.9 
days ; Summer, 
93.6 days ; Autumn, 
89.7 days; Winter, 
89 days. Thus, ^ 
Spring and Sum- 
mer contain 186^ 
days ; and Autumn 
and Winter, 178| 
days; Winter be- 
ing the shortest 
season, and Sum- 
mer the longest. 

Fig. 55 will render 
this clear to the un- 
derstanding of the student. The diagram shows the position of the earth 
when the sun is at the solstices and equinoxes, respectively, and the unequal 
portions into which the orbit is divided by the lines joining these points, 
corresponding to the unequal periods of time mentioned above. 

c. Motion of the Line of Apsides. — The line of apsides of the 
earth's orbit does not always remain in the same position in space, but 
slowly moves toward the east, about llf" every year ; hence, making a 
complete circuit in about 110,000 years. But the equinoxes are moving 
the other way about 50" every year (Art. 105 ), so that the angular dis- 
tance between the perihelion and the equinox increases annually about 
1' (more exactly, 62") ; that is to say, the longitude of the perihelion is 
about V greater at every successive year. 




'! £! mc£ 



■UNEQUAL LENGTH OF SEASONS. 



Questions. — b. What is the duration of each season ? Explain by the diagram. 
c. What motion has the line of apsides ? Its effect on the perhelion ? 



bb THE SEASONS. 

d. Length of the Seasons Variable.— The comparative length of the 
seasons is, therefore, not the same at different periods. About 6,000 
years ago, the aphelion must have coincided with the vernal equinox ; 
and hence, the seasons of summer and autumn must have been equal, 
and also those of spring and winter ; and the former must have been 
shorter than the latter. About 10,500 years ago, the earth was nearest 
to the sun in summer, and farthest from it in winter, and the seasons 
of spring and summer were the shortest, and those of autumn and 
winter the longest. This would make the summers of the northern 
hemisphere, according to the calculations of Sir John Herschel, 23° 
hotter than they now are. [Let the student modify the diagram 
(Fig. 55) so as to show each of these positions of the line of apsides]. 

e. Eccentricity Variable. — The seasons are also affected, during 
very long periods, by the variation in the eccentricity of the earth's 
orbit. At present this is diminishing at the rate of about - 2 - 6 -^ - - of the 
mean distance in a century ; that is, about 36^ miles every year ; and 
as the major axis of the orbit, and, of course, the mean distance, always 
remain the same, we are, therefore, every year 36^ miles farther from 
the sun in perihelion, and 362 miles nearer to it in aphelion, than during 
the preceding one. If this change continued for ages, the orbit would 
finally become a circle, and the seasons would be greatly changed ; 
but Lagrange, a famous French mathematician, demonstrated that 
it takes place only within very narrow limits, at the rate above men- 
tioned. If the eccentricity has continued to diminish for 80,000 years 
at this rate, at the commencement of that period, it must have been 
three times as great as at present, or about 4£ millions of miles instead 
of one million and a Jialf. The aphelion distance must then have 
been 96 millions, and the perihelion distance 87 millions. Now, the 
intensity of the solar heat varies inversely as the square of the dis- 
tance ; and the heat of the interplanetary spaces has been estimated at 
490° below zero. Hence, if we estimate the average winter heat at 
39°, the amount of heat received from the sun must be 529° ; and 
96 2 : 93 2 : : 529° : 496°. Hence, if the aphelion distance were 96 mil- 
lions of miles instead of 93 millions, the average winter heat would 
be reduced to 6°, or 26° below the freezing point. 

124. The difference of temperature in the seasons is 



Questions.— d. Effect of the motion of the apsides on the length of the seasons ? 124. 
What causes the difference of temperature during the seasons ? 



THE SEASONS. 87 

not only dependent upon the direction of the sun's rays, 
but also upon the comparative duration of day and night. 
Thus, summer occurs when the days are longest, and win- 
ter when they are shortest. 

a. All parts of the earth's surface are not affected alike by the cir- 
cumstances which produce the seasons. Those parts of the earth at 
which the sun may be vertical have the greatest heat ; those parts at 
which there may be constant night have the greatest cold ; and the 
parts between these have a degree of heat and cold not so extreme as 
either. Hence, the earth's surface has been divided into five portions, 
called Zones. 

b. The boundaries of the zones must be the circles which limit the 
declination of the sun, north and south, and those within which there 
may be constant day or night ; that is, the tropics and polar circles. 

125. The Zones are the five divisions of the earth's sur- 
face bounded by the tropics and polar circles. They are 
called the Torrid, North Temperate, South Temperate, 
North Frigid, and South Frigid Zones. 

126. The Tokrid Zone includes the space between the 
tropics, the equator passing through the middle of it. It is 
47 degrees wide. 

127. The Temperate Zones are Fi s- 56 - 
those which are included between the 
tropics and polar circles. The north- 
ern is called the North Temperate 
Zone; and the southern, the South 
Temperate Zone. Each is 43 degrees 
wide. 

128. The Frigid Zones are those 
included within the polar circles. TI ™ Z0NE8 ' 
That in the arctic circle is called the North Frigid Zone ; 




Questions.— a. Why has the earth's surface heen divided into zones? 125. Define 
the zones. How named? 126. Where is the torrid zone? 127. Where are the tem- 
perate zones? 128. The frigid zones ? 



88 



THE EARTH 



that in the antarctic circle, the South Frigid Zone. Each 
extends 23 1 degrees from the pole, and is 47 degrees. across. 



, 



SECTION VI. 



THE FIGUEE AJfD SIZE OF THE EARTH. 

129. The figure of the earth is that of an oblate 
spheroid, differing but slightly from a perfect sphere. 

a. Proofs that the Earth is Spheroidal. — Several and diverse 
proofs may be given to establish this fact. 

1. The effect of the centrifugal force would necessarily give it this 
form ; for, since this force causes bodies to fly off from the centre of 
motion, the water, or any other yielding materials of which the earth 
is composed, would recede as far as possible from the axis of rotation, 
and thus passing from the poles to the equator, cause the earth to 
bulge out at those parts. Sir Isaac Newton, from this consideration, 
very nearly ascertained the amount of oblateness in the earth's figure, 
before any actual discovery of it had been made. 

Fig. 57. This change in the form 

of a rotating body may be 
illustrated by an apparatus 
represented in Fig. 57. This 
consists of one or more cir- 
cular hoops of an elastic ma- 
terial, fastened at the lower 
end of the axis, but free to 
move up and down, at the 
upper end. TYhen set in 
rapid rotation, they lose 
their circular form and are 
bulged out at the points 
farthest from the axis, so as 
to become elliptical in form. 

2. Tlie attraction exerted by the earth at its surface is less at the equa- 
tor tJicin at any other part, and increases as ire go from the equator 
toward either of the poles. This is shown by a pendulum's vibrating 

Qitestioxs.— 1-29. What is the figure of the earth? a. What is the first proof* 
niustrate it and explain by the diagram. What is the second proof? 




THE EARTH. 



89 



less rapidly at the equator than at places nearer the poles ; and this 
can be accounted for only by supposing that the equatorial parts of the 
earth are the farthest from its centre, and the poles the nearest to it ; 
since the attraction of gravitation diminishes as the distance increases. 
3. The length of a degree on the meridian is different in different 
latitudes, showing a variation in the curvature of the earth's surface at 
different parts. If the earth were an exact sphere, the meridians would 
be perfect circles, and consequently of the same curvature at every part ; 
hence, if we find, by exact measurement, that the curvature is not the 
same, we know that they are not exact circles. This is what has been 
ascertained. The length of a degree on the meridian has been measured 
at different latitudes ; and it has been found that it is longer the nearer 
we go to the poles, showing that the earth is flattened at these parts. 

Let the ellipse, Fig. 58, repre- 
sent the form of the earth. Since 
the curvature at P is much less 
than that at E, the radius of the 
curve a b will be longer than that 
of c d ; hence, if the angle a o bis 
equal to the angle e m d, the arc a b 
which is farther from the centre 
than c d, must be the longer. Of 
course, this would be equally true 
of an angle of 1° ; and thus, the 
arc subtending one degree of an- 
gular measurement at the poles 
must be longer than the corre- 
sponding arc at the equator, if the earth is spheroidal. 

6. To Find the Size of the Earth. — The angular distance of two 
places situated under the same meridian, measured from the earth's cen- 
tre, is the arc of the meridian contained between the places. This angle 
is found by observing the change of position, with respect to the hori- 
zon or zenith, which a star appears to undergo when viewed from two 
different points on the earth's surface, one being exactly north of the 
other. The apparent displacement of the star is the angular distance, 
or meridian arc, contained between the two places. Then, having 
measured the distance in miles between the places, we can find by a 




Questions.— How is this fact shown? What is the third proof? Illustrate it. 
Explain by the diagram, b. How is the size of the earth found ? Explain by the 
diagram. 



90 



THE EARTH. 



/ 



/ 



/ 




simple proportion, the circumference of the earth. For, suppose the 
angular distance is founcf to be Zj°, and the actual distance 172.76 
miles ; then 2^° : 360° : : 172.76 miles : 24,877 miles. This must be the 
circumference of the earth ; and dividing 24,877 miles by 3.1416, the 
ratio of the circumference to the diameter, we obtain its diameter. 

To understand why 
a change in the place 
of the spectator causes 
a displacement of the 
star, let E (Fig. 59) 
represent the centre of 
the earth, P and P 
places on the earth, Z 
and 7J the zenith of 
each respectively, S, 
\ the direction of a star 
situated at an immense 
distance beyond. At 
P, the zenith distance 
of the star is a c, or the angle S P Z ; at P, the other place, it is o d, or the 
angle S P Z', greater than S P Z by the angle e P d, which is equal to the 
angle PEP. Thus, the star appears farther from the zenith Z' than 
from Z at P by the arc of the meridian, P P. 

130. The ohlateness of the earth's figure is equal only to 
■3 £(j part of its diameter, or 26^ miles. 

a. So small is this variation from an exact sphere, that if a body 
were made of the precise form of the earth, having its longest diame- 
ter three feet in length, the shortest would be only one-eighth of an 
inch less, — an amount entirely imperceptible. 

b. The longest diameter of the earth is 7,925| miles ; the shortest 
diameter 7,899 ; the mean diameter 7,912 miles. 

131. The spheroidal figure of the earth is the cause of the 

precession of the equinoxes. 

a. Precession Explained. — For since this excess of matter at the 
equator is situated out of the plane of the ecliptic, the attraction of 



Questions. — 130. What is the degree of ohlateness of the earth ? Illustration ? 
6. What are the exact dimensions of the earth ? 131. What does the spheroidal figure 
of the earth cause ? a. Explain how precession is caused ? 



THE EARTH 91 

the sun and moon acts obliquely upon it, and thus tends to draw the 
planes of the equinoctial and ecliptic together ; which tendency, by 
the rotation of the earth on its axis, is converted into a sliding move- 
ment, as it were, of one circle upon the other, both preserving very 
nearly the same inclination. 

Fig. 60. 



-©s 




Thus (Fig. 60) the attraction of the sun, acting obliquely upon the protu- 
berance, or excess of matter, at E and E', tends to draw it toward the plane 
of the ecliptic ; and this it would finally accomplish were the earth's rota- 
tion suspended ; so that the plane of the equator would be made to 
coincide with that of the ecliptic. But the effect is a sliding of the equator 
over the line of the ecliptic, and thus a change of the points of inter- 
section. 

b. Revolution of the Poles. — Since the equator moves round on 
the ecliptic, the poles of the earth must revolve around those of the 
ecliptic, and consequently change their apparent position among the 
stars. Hence, the star which is now so near the north celestial pole 
will not always be the pole-star; but in about 13,000 years, that is, 
one-half the period of an entire revolution, will be 47° from it. 

c. Why the Equinoctial Points move toward the West. — It may 
not be obvious why the equinoctial points move toward the west ; but 
perhaps the following diagram and explanation will render it clear : 

Let E E (Fig. 61) represent the equator, and e e the ecfiptic, A the first 
degree of Aries, or vernal equinox ; a b the amount of force exerted to 
draw the equator*toward the ecliptic in a given time, and ad the amount 
of rotation performed in that time. By the principle of resultant motion, 
the excess of matter and, of course, the earth with it, would move in the 

Questions. — b. Effect on the position of the poles ? c. Why does the equinox mova 
toward the west ? Explain by the diagram (Fig. 61), 




diagonal a c, thus changing the direction of the equator from E E to g h 
and causing the point of intersection to recede from A to A'. It will be 
obvious that the angle of inclination at A must be very nearly equal to 
that at A'. 

d. Obliquity of the Ecliptic Variable. — There is a very slow dimi- 
nution of the obliquity of the ecliptic, amounting to 46V * n a century. 
At present (1867), the obliquity is 23° 27' 24". The limit of the varia- 
tion is 1° 21', to pass through which arc it requires about 10,000 years. 



SECTION VII. 

TIME. 

132. The apparent motions of the sun and stars, caused 
by the real motions of the earth, afford standards for the 
measurement of time. 

133. The time which elapses between a star's leaving the 
meridian of a place until it returns to it again is called a 

SIDEBEAL* DAT. 

a. This is the time of one complete revolution of the celestial 
sphere, and is the exact period of one rotation of the earth on its axis. 
It is an absolutely uniform standard, having undergone not the 
slightest appreciable change from the date of the earliest recorded 



* From the Latin word sidus, which means a star. 



Questions. — d. What change takes place in the obliquity of the ecliptic ? 132. What 
are the standards for measuring time ? 133. What is a sidereal day ? a. Is it uniform ? 



TIME. 



93 



observations. Indeed, it is the only absolutely uniform motion ob- 
served in the heavens. 

134 A Solae Day is the period which elapses from 
the sun's leaving the meridian of a place until it returns to 
it again. 

a. As the sun is constantly changing its place among the stars, 
owing to the annual revolution of the earth, this period must be 
longer than a sidereal day ; for the sun having moved toward the east 
during the time of a rotation, the earth must turn farther in order to 
bring the place again into the same relative position with the sun. 
This will be understood by examining the annexed diagram. 

Let 1 represent Fig 62 . 

the earth in one po- 
sition of its orbit, 
and 2 the position 
to which it advances 
during one day ; P, 
the place at which 
the sun is on the 
meridian at 1 ; P', 
the same place after 
one complete rota- 
tion, as shown by 
the parallel P' S. 
It will be evident 
that in order to 
bring P' under the 
meridian, so that 
the sun may appear 
to cross it, the earth 
will have to turn a 
space represented 
by the arc P' M, which will make the solar day so much longer than the 
sidereal day. 

135. The solar day exceeds the sidereal day by an average 
difference of four minutes. 




Questions. — 134. "What is a solar day ? a. Why are the solar days longer than the 
sidereal ? Explain by the diagram. 135. What is the average difference ? 



94 



TIME. 



136. Owing to the variable motion of the earth in its 
orbit, and the obliquity of the ecliptic, this difference is not 
the same throughout the year ; and consequently the solar 
days are of unequal length. 

Why the Solar Days are Unequal.— The first cause assigned for 
the inequality of the solar days will be easily understood, by referring to 
Fig. 62 ; since it will be at once apparent that the length of the arc P' M 
must depend upon the length of the interval between 1 and 2. If these 
intervals vary, the arcs which represent the excess over a rotation turned 
by the earth in order to bring the sun on the meridian, must also vary, and 
in the same proportion. Hence, they must be longest when the earth is 
in perihelion, and shortest when it is in aphelion. 

Fig. 63. 

The second cause, 
namely, the obliquity 
of the ecliptic, needs 
an independent .illus- 
tration:— Let API 
(Fig. 63) represent 
the northern hemi- 
sphere; A E I the 
equinoctial, and A e 
I the ecliptic. Let 
the ecliptic be divid- 
ed into equal por- 
tions, Ab,bc,cd, etc., and draw meridians through the points of division, 
intersecting the equinoctial in B, C, D, etc. The divisions of the ecliptic 
will be equal arcs of longitude, and the divisions of the equinoctial will be 
the corresponding arcs of right ascension, and hence passed over by the sun 
in equal periods of time. These arcs of right ascension, it will be apparent, 
are not equal ; for A &, which is oblique to AB, must subtend a smaller arc, 
A B, than d e which is nearly parallel to its arc D E. Thus the arcs of right 
ascension are shortest at the equinoxes, and longest at the solstices; 
while the divisions coincide at all these four points. 

137. A Mean Solae Day is the average of all the solar 
days throughout the year. It is divided into twenty-four 
hours, and commences when the sun is on the lower meridian, 
that is, at midnight. 

Questions. —136. Why are the solar days unequal ? Explain by the diagrams. 137. 
What is a mean solar day ? 




TIME. 95 

a. Because used for the general purposes of civil and social life, it 
is also called the civil day. Clocks are regulated to show its beginning 
and end, and the equal division of it into hours, minutes, and seconds. 
As already stated, it is four minutes longer than a sidereal day. 

b. If the solar days were equal in length, the sun would always he 
on the meridian at 12 o'clock ; that is, apparent noon would coincide 
with mean noon — the noon of the clock. But this is not the case, and 
therefore to make the observed noon, as indicated by the sun, corre- 
spond with the noon of the clock, a correction has generally to be 
made, either by adding or subtracting a certain amount of time. This 
correction is called the equation of time. 

138. The Equation of Time is the difference between 
apparent and mean time ; that is, the difference between 
time as shown by the sun, and that shown by a well-regu- 
lated clock. 

a. The unequal motion of the earth in its orbit causes the sun to 
be in advance of the clock from aphelion to perihelion, that is, from 
July 1st to January 1st ; and behind it from January 1st to July 1st ; 
while they both coincide at those points. The obliquity of the ecliptic 
causes the sun to be in advance of the clock from Aries to Cancer, 
behind it from Cancer to libra, in advance again from Libra to Capri- 
corn, and behind again from Capricorn to Aries ; and makes them 
both agree at those four points. To verify this let the student exam- 
ine Fig. 63. When these two causes act together, as is the case in 
the first three months and the last three months of the year, the equa- 
tion of time is the greatest. 

139. The equation of time is greatest in the beginning of 
November, the sun being then about 16| minutes in advance 
of the clock. 

a. Hence, to deduce true noon from apparent noon, at that time it is 
necessary to subtract 16^ minutes from the observed time. The sun is at 
the greatest distance behind the clock about February 10th, the equation 

Questions.— a. Why called a civil day ? b. What is meant hy apparent and mean 
noon ? Do they coincide ? 138. What is the equation of time ? a. When is the sun 
in advance of the clock ? When behind it ? 139. When is the equation of time the 
greatest ? 



96 TIME. 

being then 14£ minutes, and, of course, to be added, in order to find 
the correct time. 

140. Mean and apparent time coincide four times a year, 
namely ; April 15th, June 15th, September 1st, and Decem- 
ber 24th. The equation of time then becomes nothing. 

b. To Find the Equation of Time by the Globe.— The part of 
the equation of time that depends upon the obliquity of the ecliptic 
can be found by the globe, in the following manner :— Bring the sun's 
place in the ecliptic to the brass meridian, and find its longitude and 
right ascension ; the difference reduced to time (counting four minutes 
to a degree), will be the equation. If the right ascension exceed the 
longitude, the sun is slower than the clock ; if the longitude exceed 
the right ascension, the sun is faster than the clock. 

Thus, on the 28th of January, the longitude of the sun is about 308°, the 
right ascension 310|° ; hence the sun is 10 minutes slower than the clock. 
Questions.— What is the equation of time October 19th ? Ans. Sun 10 
minutes faster than the clock. 
What is it August 13th ? Ans. Sun 8 minutes slower than 
the clock. 

141. A Sideeeal Yeae is the period of time that 
elapses from the sun's leaving any star until it returns to 
the same again. 

a. This is the true period of the annual revolution of the earth, 
and is equal to 365 days, 6 hours, 9 minutes, 9 seconds. Owing, how- 
ever, to the precession of the equinoxes, the sun advances through all 
the signs, from either equinox to the same again, in a shorter period. 

142. A Teopical Yeae is the period that elapses from 
the sun's leaving the vernal equinox until it arrives at it 
again. It is 20 min. 20 sec. shorter than the sidereal year. 

a. Its length is, therefore, 365 d 5 h 48 m 49* which is the civil year, or 
the year of the calendar, deducting the 5 h 48 m 49 s ; and as this is 
very nearly one-fourth of a day, one day is added every fourth year, 

Questions. — 140. When is the equation of time nothing ? 141. What is a sidereal 
year ? 142. What is a tropical year ? How much shorter than a sidereal year ? a. 
What is its length ? What other names has it ? 



QUESTIONS FOB EXEECISE. 97 

which makes what is called leap year, or bissextile. The tropical 
year is sometimes called an equinoctial or solar year. 

b. The sidereal year is not exactly the period which the earth 
requires to pass from perihelion to perihelion again, since the perihe- 
lion is moving slowly toward the east (Art. 123, c). This period is 
called the anomalistic year. It is about 4| minutes longer than the 
sidereal year. 

QUESTIONS FOR EXERCISE. 

These questions are to be answered by applying the principles explained 
in the preceding sections, and without the use of the globe. 

1. What is the latitude of the north pole ? 

2. What is the latitude of a place under the equator ? 

3. New York is about 49^ degrees from the north pole ; what is its 
latitude ? 

4. How many degrees is it from the south pole ? 

5. What is the latitude of a place under the Tropic of Cancer ? 

6. What under the Antarctic Circle? Under the Tropic of Cap- 
ricorn ? 

7. What is the greatest altitude of a heavenly body ? 

8. Where is the altitude greatest ? Where is it least ? 

9. If the zenith distance of a body is 15°, what is its altitude ? 

10. How many degrees wide is the circle of perpetual apparition in 
the latitude of New York ? 

11. How wide is it at the north pole ? At the equator ? 

12. If the declination of a star is 60° N., does it ever set in New York ? 

13. Does it rise in latitude 30° S. ? 

14 At what points is the declination of the sun greatest ? 

15. At what points is its decimation nothing ? 

16. What is the right ascension of the sun in the first degree of Can- 
cer? What in the first degree of Capricorn? In the first degree of 
Libra ? In the vernal equinox ? 

17. What is the longitude of the sun in the summer solstice ? In the 
winter solstice ? In the autumnal equinox ? 

18. When the sun is in either of the equinoxes, what is its merid- 
ian altitude in New York ? In London ? At Cape Horn ? At North 
Cape? 

Questions. — b. What is an anomalistic year ? Why longer than a sidereal year ? 



98 QUESTIONS FOR EXERCISE. 

19. What is the greatest meridian altitude of the sun in New York ? 
What is the least? 

20. If the declination of a star is 30° N., what is its meridian alti- 
tude in New York ? Its zenith distance ? 

21. What must its declination be to be seen in the zenith at New 
York? 

22. When is it longest day in New York ? At Cape Horn ? 

23. If a star were seen on the meridian 40° from the zenith, what 
would be its altitude, azimuth, and amplitude ? 

24. If the meridian altitude of a star in Havana is 50°, what is its 
declination ? 

25. What are the amplitude, azimuth, zenith distance, and altitude 
of a star just rising 15° from the east ? 

26. What is the right ascension of the sun when its declination is 
23i°S.? 

27. What is its declination when its longitude is 90° ? 

28. What is its right ascension when its longitude is 180° ? 

29. Where is a planet situated when its latitude is 0° ? 

30. In what position is Mars when it has the same longitude as the 
sun? 

31. At what point of a planet's orbit is the centripetal force greatest ? 
The centrifugal force ? 

32. If the inclination of the earth's axis had been 30°, how wide 
would each of the zones have been ? 

33. If it had been 45°, how wide would the torrid zone have been ? 
The temperate zones ? 

34. If the earth's axis were perpendicular, where would perpetual 
summer prevail ? Perpetual winter ? 

35. What would be the seasons, if the earth's axis coincided with 
the plane of the ecliptic ? 

36. Is constant day as long at the south as at the north pole ? 



CHAPTER VIII. 

THE SUN. 

143. The Sun" is the source of light and heat to all the 
other bodies of the solar system, and the support of life and 
vegetation on the surface of the earth, or any of the other 
planets. 

All the forces displayed on our planet, whether mechanical, chem- 
ical, or vital, spring from the sun and his exhaustless rays ; and yet, 
it is calculated, that the earth, with its limited grasp, only receives the 
two hundred and thirty millionth part of the whole force radiated and 
dispensed by this vast and splendid luminary. 

144. The greatest distance of the sun from the earth is 
very nearly 93 millions of miles ; and its least distance 
about 90 millions ; making the mean distance, as previously 
stated, about 91^ millions. 

a. History of its Discovery. — The distance of the sun from the 
earth has been, from the earliest times, a subject of close and earnest 
investigation to astronomers. Ptolemy and those contemporary with 
him, and in more modern times Copernicus and Tycho Brahe, supposed 
it to be equal to only 1200 times the radius of the earth, or less than five 
millions of miles ; Kepler thought it to be about fourteen millions of 
miles ; Halley, sixty-six millions ; and it was not until the middle of 
the last, century (1769), that any reliable determination of this impor- 
tant fact was reached. This was accomplished by finding the horizontal 
parallax of the sun by means of observations made at different parts 
of the earth, of the transit of Venus, which took place in that year. 

Questions.— 143. What is the sun ? 144. What is its distance from the earth ? a. 
Opinions of various astronomers ? 



100 THE SUN. 

b. When an inferior planet happens to be at or near one of its 
nodes, at the time of inferior conjunction, it appears like a round black 
spot on the disc of the sun, and moves across it from east to west. 
This passage across the disc is called a transit. The transits of Venus 
have been of very great interest because employed to determine the 
solar parallax. The method will be explained hereafter. 

145. The distance of the sun from the earth is ascertained 
by finding its horizontal parallax. According to a recent 
determination, this is a little less than 9". 

a. This has been found by a series of observations on Mars, made at 
the time of its opposition in 1860 and 1862, it being in those years at 
about its nearest point to the earth. More exactly stated, the solar 
parallax is 8. 94". 

b. It has been already shown (Art. 87, a.), that the angle of parallax 
varies with the distance. The method of determining the distance from 
the parallax is as follows : 

Fig. 64. Let E (Fig. 64) repre- 

, P sent the centre of the 

earth, P, a place on its 
surface, and S, the cen- 
tre of the sun. Then 
P S E is the angle of 
horizontal parallax, or 
the angle which the ra- 
dius of the earth subtends at the distance of the sun. Now, in every right- 
angled triangle, such as P S E, the ratio of either side to the hypothenuse 
depends on the angle opposite the side ; so that however long the sides of 
the triangle may be, the ratio is the same, provided the angle is the same. 
Hence, as tables have been calculated containing the ratio of every possi- 
ble angle, we can always find, by referring to these tables, this ratio when 
we know the angle. In the triangle S P E, S E, the hypothenuse, is the 
distance of the sun, and P E, the radius of the earth, equal to 3956 miles. 
The opposite angle P S E, is the horizontal parallax, or 8.94". For this 
angle we find the ratio to be about .0000432; that is, P E = S E X .0000432 ; 

P E 
and hence S E = 7^0432 ' but 3956 "*" • 0000433 = 91,574,074, which is about 

the mean distance of the sun. 

QiresTioNS. — b. What is a trannf ? 145. How is the distance of the sun found ? a. 
What is the solar parallax ? b. How is the distance of the sun deduced from the par- 
allax ? 




THE SUtf. 101 

C. The ratio of either side of a right-angled triangle to the hypoth- 
enuse, dependent upon any particular angle, is called the sine of that 
angle. Thus, the sine of 30° is .5 or f ; that is, if one of the angles of 
a right-angled triangle is 30°, the side opposite that angle will be one- 
half the hypothenuse. 

d. Hence, it may be given as a general rule, that the radius of the 
earth divided by the sine of the horizontal parallax of any tody is equal 
to its distance from the earth. 

Note. — It is important that the student should keep the above definition 
and rule in memory, as they will be employed in several subsequent calcu- 
lations. 

146. The apparent diameter of the sun, or the angle 
which it subtends in the celestial sphere, is about 32', or a 
little more than one-half of a degree. 

a. This is the mean value ; the greatest being 32' 86" ; and the least 
31' 32". This variation in the apparent size of the sun is caused by 
the elliptical orbit of the earth ; it being greatest when the earth is 
in perihelion, and least in aphelion. The apparent diameters of the 
sun, at different periods of the year, are measures of the different 
lengths of the radius-vector of the earth's orbit, and thus lead to a 
knowledge of its exact figure. 

b. Since the greatest apparent diameter is 32.6', and the least 31.533', 
their ratio Is as 1.034 to 1 (nearly), and one-half the difference, or .017, 
is about the eccentricity of the earth's orbit. 

147. The actual diameter of the sun is 852,900 miles, or 
107f times the diameter of the earth. 

a. This is found by a calculation based upon the principle of the 
right-angled triangle, explained in Art. 145. The method is as fol- 
lows: 

Let S(Fn?. 65) be the centre of the sun, E the place of the earth. Then S A 
E is a right-angled triangle, in which the hypothenuse SE is the distance of 
the sun from the earth, A S the radius of the sun, and the angle A E S 

Question^.— c. What is the sine of an angle? d. Give the general rule. 146. 
What is the apparent diameter of the sun ? a. How does it vary ? ft. How may the 
eccentricity of the earth's orbit he found? 14T. What is the actual diameter of the 
sun ? a. How found ? Explain from the diagram. 



102 



THE SUN. 




one-half the apparent 
diameter, or 16'. The 
ratio corresponding to 
this angle, or the sine 
of the angle, is .00466 ; 
hence, 91,500,000 X 
.00166 = 426,390, the 
semi-diameter of the 

sun ; and, therefore, the diameter is 852,780 miles, which is very nearly its 

exact length. 

148. The figure of the sun appears to be that of a perfect 
sphere, no observations having as yet detected any indica- 
tions of oblateness. 

a. Surface and Volume. — Since the surfaces of spheres are as the 
squares of their diameters, and the volumes as the cubes, it follows 
that the surface of the sun must be 11,620 times that of the earth, and 
its volume 1,252,000 times ; or, in round numbers, one million and a 
quarter of worlds as large as the earth must be rolled into one to form 
a body of the bulk of the sun. 

149. The mass of the sun is 315,000 times as great as 
that of the earth. 

a. The method of finding this will be explained in a subsequent 
article. Since the volume of the sun is 1,252,000, while the mass, or 
quantity of matter is only 315,000, as compared with the earth, it fol- 
lows that the density of the sun must be only \ that of the earth. 
Now, the earth's density has been found by certain experiments to be 
about 5£ (5.67) times that of water ; hence, that of the sun must be less 
than 1\ that of water (1.42). 

b. From the comparative lightness of its substance, Herschel infers 
that an intense heat prevails in its interior, imparting an expansibility 
sufficient to resist the force of gravitation, which, otherwise, would 
cause the body to shrink into smaller dimensions. 

c. The volume of the sun is, as already stated, about 500 times that 
of all the planets ; the mass is, however, about 700 times as great. 



Questions.— 148. What is the figure of the sun ? a. What is said of its surface and 
volume ? 149. What is its mass ? a. Its relative mass and density ? b. What is 
the inference drawn hy Sir John Herschel ? c. Mass of the sun compared with that 
of the planets ? 



THE SUE". 



103 



This shows that the mass of the sun is greater than the average mass 
of the planets. 

150. The sun rotates from west to east on an axis nearly 
perpendicular to the plane of the ecliptic, the period ot 
rotation being about 25J days (25 d 7 h 48 m ). 

151. This is proved by the spots which are seen upon its 
disc, and which appear to move across it, occupying about 
two weeks in their passage. 

Fig. 76. 




A SPOT PASSING ACBOSS THE DISC. 

a. A particular spot which can be identified by its appearance first 
appears on the eastern limb, or edge, of the disc, passes across to the 
western limb, and then disappears ; but after about two weeks, re-ap- 
pears on the eastern limb, completing an entire revolution in about 

Fig. 67. 




MOVEMENT OP THE SXTN AND SPOTS. 



27i days. But this must be longer than the period of a rotation, 
because the earth is moving in its orbit in the same direction. When, 



Questions. — 150. Does the sun rotate? 151. How is this known ? a. How do the 
spots move ? Their time of rotation ? How to find the time of the sun's rotation ? 



104 



THE SUN. 






therefore, the earth has completed one revolution, the number of revo- 
lutions of the spots will be one less than the actual number of 
rotations of the sun for the time. Hence, 365^ days -r- 27i days = 13.4, 
revolutions of spots ; and 13.4 + 1 = 14.4, rotations of the sun ; there- 
fore, 365^ days -J- 14.4 = 25^ days, the time of one rotation. (See Fig. 67). 

b. It may appear singular, at the first view, to infer an eastward rota- 
tion of the sun from an apparent westward motion of the spots ; but 
it must be remembered that the sides of the sun and earth presented 
to each other at any time are moving in opposite directions in space, 
while both bodies move in the same direction in circular motion. 

c. Discovery of the Spots. — The discovery of spots on the solar 
disc is noticed in history as early as 807 A. D. ; but their true appear- 
ance and extent were unknown until the invention of the telescope, in 
the beginning of the 17th century, at which time (in 1611) they were 
attentively observed by Galileo and others. In recent years, the sun 
has received a very great deal of attention from astronomers, and 
many interesting facts have been made known respecting its appearance 
and physical constitution. 

152. The inclination of the sun's axis to the ecliptic is 
7|° ; and, in consequence of this inclination, the spots 
appear to move across the disc in lines of various directions 
and form, sometimes being straight and sometimes curved. 

Fig. 68. 

MARCH JUNE 






APPABENT PATHS OF SOLAS SPOTS. 



Fig. 68 illustrates this. In March, when the south pole is presented to 
the spectator, the paths assume the appearance indicated in the first circle ; 
in June, they are straight and oblique, because the observer is in the plane 



Questions.—! 
their discovery j 



Why do the spots seem to move from east to west? c. History of 
152. What is the inclination of the sun's axis? 



THE SUN, 



105 



of the sun's equator ; while in September, the observer being north of its 
equator, the north pole is turned toward him, and they are as represented 
in the third circle. [The inclination of the axis is exaggerated in the 
diagram.] 

153. Appearance of the Spots. — When the spots are 
examined by means of a telescope, they present the appear- 
ance of irregular black patches surrounded with a dusky 
border or fringe, the whole sometimes encompassed with a 
bright surface or ridge. The black portion in the centre is 
called the umbra or nucleus ; the dusky border, the penum- 
bra ; and the bright surfaces seen around the spots, or by 
themselves on other parts of the disc, are called faculm. 

FiT 69. 








■> 



8 OL AB SPOTS. 



a. Sometimes the nucleus is absent ; and sometimes spots are seen 
without any penumbra. The nucleus is not of a uniform blackness, 
but generally contains an intensely black spot in the centre. These 
spots usually appear in clusters, numbering from two to sixty or sev- 
enty, or even many more. 

154. Variability of the Spots.— The solar spots con- 
stantly undergo very great changes in number, form, size, 
and general appearance. 



Questions.— 153. Explain the appearance of the spots, 
appearance ? 154 What changes do they undergo ? 



What diversity in their 



106 THE SUN. 

a. Sometimes the sun's disc will be entirely free from them, and 
will continue so for weeks and months ; at other times, they will burst 
forth and spread over certain parts of it in great numbers. After 
twenty-five years of continued observations, M. Schwabe, a German 
astronomer, discovered that there was a periodical increase and de- 
crease of the number and size of the spots ; and Prof. Wolf, of Zurich, 
by comparing the observations made during the last hundred years, 
has shown that this period has varied between 8 and 16 years. These 
periods are thought by some to depend upon physical influences exerted 
by some of the planets, particularly Venus and Jupiter, when in cer- 
tain positions of their orbits. 

Fig. 70. 







SUN-SPOT, JTTLT 29, 1860, STTOWING THE " WILLOW-n^P" STETTCTtTBE. 

6. The spots are mostly confined to two zones parallel to the equator, 
and extending from 5° to 35° from it ; and they appear to have a tend- 
ency to arrange themselves in lines parallel to the equator. 

c. The duration of single spots is also very variable. A spot has 
been seen to make its appearance and vanish within twenty-four 



Questions.— or. What ppriods have heen established? b. To what zone are the 
spots mostly confined ? c. Their duration ? 



THE SUN. 107 

hours ; while others have continued for nine or ten weeks, without 
much change of appearance. 

d. Their magnitude also presents very great diversity. Spots are 
not unfrequently seen that subtend an angle of more than 60", or 
nearly seven times the sun's horizontal parallax ; the diameter of such 
spots must therefore be more than 25,000 miles. A spot in June, 1843, 
continued visible to the naked eye for a whole week, its length being 
estimated at 74,000 miles. One observed in 1839, by Capt. Davis, had 
a linear extent of 186,000 miles. 

Fig. 70 represents a large spot as seen and drawn by Mr. Nasmyth, an 
English astronomer, hi 1860. It shows the umbra, penumbra, the latter 
arching the former as well as surrounding it, and also the dotted or mottled 
surface of the sun, as seen through a powerful telescope. The penumbra 
presents the appearances to which Mr. Nasmyth has applied the name of 
"willow leaves," from their fancied resemblance to such objects. 

• 155. Theokies as to the Physical Constitution of 

the Sun. — The most generally received hypothesis as to 
the nature of the sun is that it is an opaque body surrounded 
by an atmosphere of luminous matter, and that the spots 
are openings in the atmc sphere, through which the dark 
body of the sun becomes visible. 

a. This hypothesis was first advanced by Dr. Wilson, of Glasgow, 
in 1769. In 1793, Sir William Herschel suggested the hypothesis that 
two atmospheres encompass the sun ; the first or lower one being 
formed of a partially opaque or cloudy stratum reflecting light, but 
emitting none of itself; and the second consisting of luminous mat- 
ter, which is the source of the sun's light, and gives to the disc its 
form and limit. This luminous atmosphere has been sometimes called 
the photosphere. 

b. The existence of a third atmosphere, very nearly transparent, 
and extendi nsr a great distance above tie photosphere, is clearly indi- 
cated by the diminished brightness of the sun's disc toward the edges. 

c. Wilson's and Herschel's hypotheses, as developed and modified 



Questions. — d. Their magnitude? 1f>5.What generally received hypothesis as to 
the cause of the spots? a. By whom advanced ? b. What evidence of a third atmos- 
phere? c. How do Wilson's and Herschel's hypotheses explain the phenomena? 
Cause of the openings ? 



108 THE SUN. 

by more recent observers, explain all the phenomena of the spots 
The black umbra is the body of the sun, while the penumbra is the 
non-luminous atmosphere, or cloudy stratum, rendered visible by the 
larger opening in the photosphere above it. When this opening is 
smaller, no penumbra is visible ; and when there is no opening in the 
cloudy stratum, no black nucleus is visible. These openings or rents 
are supposed by Sir John Herschel to be caused by changes of tem- 
perature, in a manner similar to the production of tornadoes and other 
agitations of the earth's atmosphere. 

156. The spots and other appearances on the sun's disc 
indicate, without doubt, the existence of a luminous atmos- 
phere, consisting of gaseous matter in an incandescent 
state, — like the flame of an ordinary gas-burner, — and 
another atmosphere, also gaseous, and almost perfectly trans- 
parent, extending to a considerable distance beyond. 

a. The gaseous character of the atmosphere, denied by Sir William 
Herschel, seems to have been conclusively proved by M. Arago, by means 
of an ingenious application of the principle of polarized light. M. Faye 
estimates the height or extent of the photosphere at 4,000 miles. 

b, KirchhofP s Hypothesis. — A simpler hypothesis than Wilson's 
and Herschel's has within the last five years been advanced by Kirchhoff, 
a German physicist, and others, to account for the phenomena of the 
spots, consistently with the established facts, as above stated. Accord- 
ing to this hypothesis the nucleus of the sun is an incandescent, solid 
or liquid mass, the vapors arising from which form the atmospheres, 
the denser and lower one being luminous from the incandescent particles 
that float in it. Changes of temperature in this atmosphere give rise 
to tornadoes and other violent agitations ; and descending currents pro- 
duce the openings, which are dark because filled with clouds of various 
degrees of condensation. This theory, and the experiments upon which 
it is based, are receiving, at present, much attention from astronomers 
and physicists ; and there is reason to believe, that when fully devel- 
oped, it will entirely supersede the cumbrous and therefore improbable 
hypothesis so long and so inganiously sustained. 



Questions. — 156. What, is certainly indicated by the phenomena f a. Gaseous char* 
acter of the atmosphere ? b. Explain KirchhofFs hypothesis. 






THE SUN 
Fig. 7L 



109 



VtJfV * EARTH 

jl^^fc. -<-~ MARS 

• •• 



• • 



APPAEENT MAGJTITTTDES OP THE 8TTS. 

157. The apparent diameter of the sun at each of the 
planets diminishes in proportion as the distance increases. 
Thus, at Mercury, it is 2^ times as great as at the earth ; 
but at Neptune, only 3^ as large. 

a. The surface of the solar disc at Mercury must therefore be 
about 6,000 times as great as at Neptune, and the intensity of its 
light and heat in the same proportion. 

6. Various experiments seem to show that the light of the sun at 
the earth is equal to that of 600,000 full moons ; (Wollaston estimated 
it at 800,000.) The light of the sun at Neptune must therefore be 
equal to about 670 times that of the full moon at the earth. The 
electric light is the only light that approximates in intensity to the 
light of the sun. 

c. The intensity of heat at the surface of the sun has been esti- 
mated to be 300,000 times that received at any point of the earth's sur- 
face. Sir John Herschel supposes that it would be sufficient to melt a 
cylinder of ice 45 miles in diameter, plunged into the sun, at the rate 
of 200,000 miles a second. 

158. In addition to the rotation on its axis, the sun 
appears to have a progressive motion in space, revolving 
with all its attendant bodies around some remote star or 
centre. 

Questions. — 157. How does the sun appear at the different planets? a. Its surface, 
light, and heat, at Mercury and Neptune ? 6. Light of the sun ? c. Intensity of its 
heat? 153. Motion of the sun and solar system in space ? 



110 



ZODIACAL LIGHT. 



a. The point to which it is tending has, from a vast number of 
observations made by different astronomers, been located in 260° 20' of 
right ascension, and 33° 33' of declination. Its annual velocity is sup- 
posed to be about 160 million of miles. 

THE ZODIACAL LIGHT. 

159. The Zodiacal Light is a faint luminous appear- 
ance, of the form of a triangle or cone, seen at certain 
seasons of the year, in the evening at the western, and in 
the morning at the eastern horizon. 

a. Its color is a faint white, tinged 
with yellow at the base, and fading 
away toward the apex, which is not 
sharp, but obtuse, or rounded. It 
extends obliquely from the horizon, 
in the plane of the sun's equator, 
and hence, very nearly in that of the 
ecliptic ; the distance of its apex 
from the sun varying from 40° to 
100° or more. Its breadth at the 
horizon also varies from 8° to 30°. 

b. It is seen most distinctly in 
March and April after sunset, and in 
September and October before sun- 
rise ; because, at those times, the 
ecliptic is most nearly perpendic- 
ular to the horizon. In tropical 

regions it is more conspicuous than in the higher latitudes, and has 
been seen at midnight at both sides of the horizon at once, extending 
upwards so as almost to form a luminous arch. 

It appeared thus to Chaplain Jones of the U. S. Navy, who, from 1853 
to 1857, made a long and careful series of observations of it at the equator 
and between the tropics. He thought the observed phenomena proved it 
to be a nebulous ring encompassing the earth. Humboldt, in the same 
latitudes, also saw the double appearance of this light. 




Questions.— a. To what point is it tending? Its velocity ? 159. What is the zodiacal 
light? a. Its color, size, and direction of its axis? b. When seen? 



ZODIACAL LIGHT. Ill 

c. Cause of the Zodiacal Light. — Various hypotheses have been 
suggested to account for the zodiacal light ; that most generally 
received at present is, that it is a nebulous mass of great tenuity, 
of the shape of a lens, encompassing the sun at its equator, and 
extending sometimes beyond the orbit of the earth. 

d. It must therefore sometimes envelop the earth in the plane of the 
ecliptic ; and consequently, to a person situated at the equator, or at 
either of the solstices, when the sun is in the other, would necessarily 
appear, about the time of midnight, at both sides of the horizon ; while, 
f.irther north or south, it would disappear at that time, because viewed 
at a lower altitude, and through its narrowest part ; and would there be 
visible only in the evening, near the sun, where the line of view would 
penetrate it at its greatest thickness. 

e. Professor Norton regards it as made up of " streams of particles 
continually flowing away from the sun, under the operation of a force 
of solar repulsion due to disturbances occasioned by the planets in 
the magnetic condition of the particles composing the photosphere, 
and, therefore, arising from the same physical cause as that which 
produces the spots." He also traces a connection between it and the 
•luminous appearance called the corona, saen at the time of a total 
eclipse of the sun around the obscured disc. The zodiacal light, he 
thinks, " may vary in brightness from one year to another, with the 
varying activity of discharge from the sun's surface." By others it 
has been regarded as a vast ring of meteors circulating about the sun, 
and finally impinging upon it. 

/. Meteoric Theory of the Sun's Heat.— This hypothesis of a 
constant shower of meteoric bodies falling upon the sun, has been 
used to account for the support of its heat ; for their collision with the 
sun would necessarily generate an intense heat, just as iron may be 
heated to any degree by hammering it. It is calculated that bodies of 
the density of granite falling all over the sun to the depth of 12 feet 
in a year, and with the velocity which they would acquire (384 miles 
in a second), would maintain the solar heat If Mercury were to strike 
the sun, it would generate an amount of heat equal to all the sun emits 
in seven years ; while the shock of Jupiter would supply the loss of 
more than 30,000 years. 



Questions.— c. How is the zodiacal light explained ? d. TTowis the luminous arch 
explained ? e. Professor Norton's opinion ? /'. Theory to account for the sun's heat f 



CHAPTER IX. 

THE MOOX. 

160. The Moon, although one of the smallest bodies in 
the solar system, is, to us, next to the sun, the most con- 
spicuous, interesting, and important, on account of its close 
connection with our own planet, and the effects which it 
produces upon it. 

161. The orbit of the moon is elliptical ; the point nearest 
to the earth being called the pekigee,* and the point 
farthest from it, the apogee, f 

162. Its mean distance from the earth is 238,800 miles ; 
and it is 26,000 miles nearer to us in perigee than in apogee. 

a. Its eccentricity is, therefore, 13,000 miles, or about .055 of its 
mean distance. This is more than three times as great, in proportion, 
as that of the earth, which is less than .017. 

h. To Find its Distance. — The distance of the moon is found by 
the method and rule explained in Art. 145. The moon's mean hori- 
zontal parallax is 57', the sine of which is .01657 : hence, 3956 h- .01657 
= 238,745 ; which is very nearly the distance found by exact com- 
putation. 

c. This is the distance of the moon from the earth's centre ; conse- 
quently it is about 4,000 miles nearer to a point of the earth's surface 



* From the Greek words peri, meaning near, and gee, the earth. 
t From the Greek words apo, meaning from, and gee, the earth. 

Questions.— 160. What is the moon? 161. What is perigee? Apogee? 162. The 
mean distance of the moon ? How much greater in apogee than in perigee ? a. The 
eccentricity of the moon's orbit ? ft. How to calculate the distance? c. The distance 
of the moon at the horizon and in the zenith ? 



THE MOON. 113 

directly under it ; and, with reference to any particular place on the 
surface of the earth, its distance varies with its altitude, being greatest 
at the horizon, and least at the zenith ; that is, about 4,000 miles 
farther in the horizon than when in the zenith. 

Thus (Fig. 73), when the moon is at A, in Fig. 73. 

the horizon, its distance from the place P is q 

A P ; but at B, in the zenith, it is B P ; and ^— — Q— «^^ 

A P is obviously greater -than B P by y^ ^v 

nearly the radius of the earth, or about / \ 

4,000 miles. / P\ V A 

d. Motion of the Apsides. — Theposi- / ( j N 

tions of the apogee and perigee in space £ 

are determined by noticing when the moon's apparent diameter is 
greatest and when least. Careful observations of this kind show that 
these points shift their positions, and that the line of apsides completes 
a circuit from west to east in 8? 310| d . This is called the progression 
of the apsides. 

163. The inclination of the moon's orbit to the plane of 
the ecliptic is about 5}° ; consequently, it crosses this plane 
in two points called the moon's nodes. 

a. Their positions are ascertained by observing from day to day the 
distance of the moon's centre from the ecliptic, which is its latitude, 
and noticing when the latitude becomes nothing. It must then be in 
one of the nodes ; when it comes from the south, the ascending node, 
and when from the north, the descending node. 

b. Motion of the Line of Nodes. — The line of nodes, like the line 
of apsides, is subject to a change, but in a retrograde direction, or 
from east to west. It completes a revolution in 18^ years. 

164. The mean apparent diameter of the moon is 31^', 
or a little more than half of a degree ; being about the 
same as that of the sun. The real diameter of the moon is, 
therefore, 2,162 miles. 

a. The Size of the Moon Calculated. — For the distance multi- 

Questions.— d. Motion of apsides? 163. The inclination of the moon's orbit? 
Nodes? a. How to determine their positions? b. Motion of line of nodes? 164. 
What is the apparent diameter of the moon ? Real diameter ? a. How found ? 



114 THE MOON. 

plied by the sine of the apparent diameter is equal to the real diameter 
(Art. 147, a). The sine of the apparent diameter is .009055, and 
238,800 X .009055 = 2162.3, which is the real diameter of the moon. 

6. Surface, Volume, Mass. — The diameter being very nearly equal 
to i 3 !- that of the earth, its surface is (vV) 2 , or yf - f > or about - 2 - 7 - of the 
earth's surface ; and its volume (A) 3 , or about -fe that of the earth. 
Its mass is estimated to be about -£$ of the earth's ; and consequently 
its density must be considerably less, about f, 

PHASES OF THE MOON. 

165. The moon, when she first becomes visible in the 
west, is seen as a slender crescent ; but from evening to 
evening her form expands as her angular distance eastward 
from the sun increases, until when in quadrature, or 90° 
from the sun, half of her disc is visible. When she has 
departed so far to the east that she rises just as the sun sets, 
the whole of her disc is seen, and she is said to be full. 
After this she becomes the waning moon, rising later and 
later, and growing less and less, until she may be seen in 
the east as a bright crescent just before sunrise. A short 
time after this she disappears, and then becomes visible 
again in the west. These different appearances, called the 
phases of the moon, prove that she revolves around the earth 
from west to east. 

166. When the moon is in conjunction, the dark side 
being turned toward us, she is called new moon ; when she 
is in quadrature and shows half of her disc, she is called 
half -moon ; when she is in opposition, she is called full 
moon. When she is in quadrature after conjunction, she is 
said to be in her first quarter ; when in quadrature after 
opposition, in her last quarter. 



Questions.— h. The surface, volume, and mass of the moon ? 165. Describe the 
phases of the moon ? 166. What is the phase in conjunction, etc. ? 




PHASES OF THE MOON 



167. When she is between conjunction and quadrature 
she assumes the crescent form, and is then said to be horned; 
when she is between opposition and quadrature, she exhibits 
more than one-half of her disc, but not the whole, and is 
said to be gibbous. 

The positions of new and full moon are sometimes called the 
syzygies* 

168. The phases of the moon are the different portions of 
her illuminated surface which she presents to the earth as 
she revolves around it. 



* From the Greek word syzygia, meaning a yoking together. 

Qtttsttoxs. — 167. When is the moon said to be horned? G-ibbous? What are the 
gyzygies ? 16S. Define the phases. 




X 



116 THE MOON. 

PiS- 75. In Fig. 75, let the par- 

5 tially darkened circle 

^^w represent the moon ; S 

the direction of the sun ; 
E, the direction of the 
earth on one side of the 
moon, and E', its direc- 
tion on the opposite side . 
Then a b will represent 
the line which separates 
the illuminated and 
darkened hemispheres of 
moon horned and gibbous. the moon ; and c d, that 

which separates the hemisphere turned toward the earth from that turned 
away from it. At E, a c being the only part of the disc visible, the moon 
appears horned ; while at E', b c being visible, the form is gibbous. 

a. Hence we can find the time of a revolution of the moon by 
observing the phases. If the earth were at rest, the time from one 
new or full moon to the next would be exactly the period of a revolution ; 
but as the earth is constantly advancing in her orbit, when the moon 
has completed a revolution, she has to move still farther in order to 
come into the same relative position with the earth and sun. 

169. The time from one new moon to the next is 29£ 
days. This is the synodic period, and is called a synodical 
month, or lunation. 

a. Sidereal Period Calculated. — In a year, or 365i days, the 
moon makes 365|-f- 29K or 12 yW synodic revolutions; but the side- 
real, or actual, revolutions of the moon must be one more ; because 
each synodic revolution is equal to one sidereal revolution and a part 
of another, equal, in angular measurement, to the advance of the earth 
in her orbit during each synodic revolution of the moon. Hence, the 
moon performs 13-,^ sidereal revolutions in 365 V days : but 3651- days 
4- 13 -th = 27i days (nearly), which is, therefore, the time of one 
sidereal revolution. 

In Fig. 76, let A B represent the advance of the earth in its orbit, while 
the moon completes a synodic revolution, that is T moves from c, the posi- 
tion of inferior conjunction, till she arrives at the same relative position 

Questions. — a. What can we find by the phases ? 169. What is a synodical month, 
or lunation ? a. How to find the sidereal period ? Explain by the diagram. 



THE moo:n t . 



IV 



with the sun at E. But when she reaches this point, she has completed a 
sidereal revolution, and has also moved from D to E, a distance, it will be 

Fig. 66. 




BIDEBEAL AND SYNODICAL EEVOLTTTION. 

seen, equal in angular measurement to AB; since the arc A B bears the 
same proportion to the earth's orbit that E D does to that of the moon. 

170. Owing to the constant advance of the moon in her 
orbit, she rises and, of course, arrives at the meridian and 
sets, about 50 minutes later each successive day. 

a. This is the average interval of time between the successive ris- 
ings of the moon ; for since she moves through the ecliptic in 29£ days, 
her daily advance is equal to about 12£° ; but a place upon the earth's 
surface moves 15° in one hour, and hence, requires nearly 50 minutes 
to overtake the moon. If the moon's orbit or the ecliptic, since the 
inclination is very small, always made the same angle with the hori- 
zon, this would be the constant interval ; but, in consequence of the 
obliquity of the ecliptic, this angle continually varies during each 
lunation. 

171. The Harvest Moon is the full moon that occurs 
in high latitudes, near the time of the autumnal equinox, in 
September and October, when she rises but a little later for 
several successive evenings, and thus affords light for col- 
lecting the harvest. 

a. By means of the globe, it may be easily shown that the ecliptic 
is most oblique to the horizon in the signs Pisces and Aries, and least 
so in Virgo and Libra ; so that when the moon is in the former signs, 
in this latitude, she rises only about half an hour later, but when in 

Questions. — 170. Why does the moon rise later each evening? a. Why are the 
intervals unequal ? 171. What is harveBt moon ? a. How to explain this phenomenon? 



118 



THE MOON. 



the latter, more than an hour. This difference is, however, only- 
noticed when the moon happens to be full while in Pisces or Aries, 
and thus rises, for several evenings, in the higher latitudes, but 
a few minutes later. These full moons must occur, of course, in 
September and October, when the sun is in the opposite signs, Virgo 
and Libra. In the former month, the full moon in England is called 
the Harvest Moon ; in the latter, sometimes, the Hunter's Moon. 



Let HSHM (Fig. 77) represent 
the horizon ; S, the position of the 
sun at sunset ; M, the full moon 
just rising ; S A M, the part of the 
equator, and S B M, the part of the 
ecliptic above the horizon, the sun 
being in Libra, the autumnal equi- 
nox, and the moon in Aries, the 
vernal equinox. Since the southern 
half of the ecliptic lies east of Libra, 
it will be evident that in or near 
this position the ecliptic must make 
the smallest angle with the horizon ; 
and consequently, while the moon 
makes her daily advance in her 
orbit, M &, she only descends below 
the horizon a distance equal to h b; while, if her orbit made a greater 
angle with the horizon, as S A M, she would, by advancing through the 
equal arc M a, descend below the horizon a distance equal to h a. 




HAEVEST MOON. 



b. In the Polar Regions, since the full moon must be opposite to 
the sun, it remains constantly above the horizon ; and during about 15 
days passes through its changes without rising or setting, appearing 
to move around the horizon ; and at the pole, in a circle exactly parallel 
to it. At the time of the solstice, it is first seen in the west in its first 
quarter, and continues constantly visible till the last quarter. These 
brilliant moonlight nights serve partially to compensate the inhabit- 
ants of those dreary regions for the long absence of the sun. 

c. Moonlight in Winter. — The moonlight nights in the temperate 
latitudes are longer and more brilliant in winter than in summer; 
especially about the time of the winter solstice. For when the sun is 
in Capricorn, 23^° south of the equinoctial, the full moon is in the op- 



Qttesttonb. — b. The moon as seen at the polar regions? c. Moonlight In winter? 



THE MOOtf. 119 

posite sign, Cancer, 23£° north of the equinoctial, and therefore 
culminates at a great altitude ; and, if she happens to be also at the 
point of her orbit, 5|° north of the ecliptic, at her greatest altitude, 
which is equal to the complement of the latitude plus 23£° plus 5\°. 
In New York, this is 49° + 23^ + 5f = 77° 38'. 

172. Observations with the telescope show that the moon 
always presents very nearly the same hemisphere to the 
earth. This proves that it rotates on its axis once during 
each sidereal month, or 271 days. 

a. The unassisted eye is able easily to perceive that the dusky 
spots on the disc of the moon constantly keep in the same relative po- 
sition and present the same appearance ; and this could not occur if 
she rotated so as to present in succession different hemispheres to the 
earth. Just as we infer a rotation of the sun from the apparent 
motion of the solar spots, so we know that the moon rotates during 
one revolution around the earth, by the observed fact that the lunar 
spots have no apparent motion ; since, if the moon performed no rota- 
tion, the spots on its disc would move across it from west to east, 
keeping pace with the moon's motion in the ecliptic, and completing 
one apparent revolution in 29^ days. 

Fig. 78. 



That the moon must perform one rotation during each sidereal month, 
in order to keep the same side turned toward the earth, will he evident 
from the annexed diagram (Fig. 78). Let the line 1, 2, 3, etc., represent 
a portion of the earth's orbit, and the dotted curve the real orbit of the moon, 
as it is carried by the earth around the sun during one lunation. When 

Questions.— 172. How do we know that the moon rotates ? a. How to explain this f 



120 THE MOON. 

the earth is at 1, the moon is full ; at 2, last quarter ; at 3, new ; at 4, first 
quarter ; and at 5, full again. The line a b indicates the position of the 
moon at the commencement of a rotation ; and the parallel line c d y its 
position if it had only completed a rotation at the end of the lunation ; but 
it is evident that in order to keep the same face to the earth at 5, it must 
have turned more than one rotation by the angle contained between c d 
and ef. Hence, during a synodic period, or lunation, the moon performs 
more than one rotation, which she completes in a sidereal period, or 27J 
days. 

173. The real orbit of the moon, as she is carried by the 
earth around the sun, crosses the earth's orbit every 14^°, 
but departs so little from it that it is always concave to the 
sun. 

a. It will be evident from Fig. 78, that the moon crosses the earth's 
orbit twice during each lunation, or 29^ days ; but there are nearly 12£ 
lunations in a year ; hence the moon must cross the earth's orbit 25 
times during one year ; and 560°- -s- 25 = 14£° (nearly). 

b. The Lunar Orbit. — The orbit of the moon, if correctly repre- 
sented in relation to that of the earth, would present the appearance 
of a continuous curve, never crossing itself, and so slightly deviating 
from the earth's orbit as, unless drawn on a very large scale, scarcely 
to be distinguished from it. This will be evident when it is considered 
that the moon's distance from the earth is only about - 4 -£- - of the earth's 
distance from the sun. Why the lunar orbit is always concave to the 
sun, will be made clear by the following diagram : — 

Let the dotted curve ABODE represent the moon's orbit crossing that 
of the earth at A, C, and E. At A, the moon is in first quarter, and west of 
the earth (although east of the sun) ; at B, it has made one-fourth of a revolu- 
tion, and is opposite to the sun and full ; at C, it is in last quarter, being 
east of the earth ; at D, it is new ; and at E, again west of the earth and 
in first quarter, having thus completed one lunation. The arc A C or C E 
being known, it it easy to compute the distance of the chord A C or C E 
from the arc. This will be found to be about 750,000 miles ; but as the 
moon's distance from the earth is only 240,000 miles, its orbit can never be 
beyond the chord, but must, as at C D E, be within it ; and hence, must be 
always concave to the sun. In the diagram, the principle only is illustrated, 



Qttestiows. — 173. Describe the real orbit of the moon. a. How often does it cross 
the earth's orbit ? b. Why always concave to tbe Bun ? Explain from the diagram. 




121 



the relative distance of the moon being greatly exaggerated, as well as the 
orbital movement of the earth during the lunation. The arc A C E in the 
diagram is more than 120° , whereas it should be only about 29°. 

c. Librations of the Moon. — As the orbit of the moon is elliptical, 
her velocity is not uniform, sometimes exceeding that of her rotation, 
and at other times exceeded by it. In consequence of this, a small 
portion of the hemisphere turned away from the earth becomes visi- 
ble alternately at the eastern and western limbs. This is called the 
Iteration* in longitude. A portion of her surface is also exhibited 
alternately at each pole, caused by the inclination of her axis to the 
plane of her orbit. This is called the libration in latitude. 

The greatest extent of the libration in longitude is 7° 53' ; in lati- 
tude, 6° 47' ; and the whole amount of the moon's surface made visible 
by both is about y^. There is also a third libration caused by the 
difference in the angle under which the moon is viewed at any place 
when on the meridian from that at which we see it when at or near 
the horizon. This is called the diurnal libration. It is, however, 
quite inconsiderable, amounting to only 32" when greatest, and bring- 
ing into view, but j-^q of the moon's surface. Hence, ■$£$,- of the 
lunar surface is all that we are ever able to see ; -ffifo having never 
been gazed at by any human eye. 



* Libration means a balancing, and is applied in consequence of the ap- 
parent rolling or vibratory motion of the moon from one side to the other. 



Questions.— c. What are librations ? Of how many kinds ? Explain each, 
much of the moon's surface have we ever been able to see? 



How 



122 



THE MOON. 



d. Position of the Lunar Axis. — The moon's axis leans toward 
its orbit 6° 39' ; hence, this is the angle which the plane of its equator 
makes with that of its orbit ; and observation determines that the 
plane parallel to the ecliptic lies between these two planes ; therefore, 
the inclination of the moon's axis to the plane of the ecliptic is equal 
to 6° 39'— 5° 8', (the inclination of the orbit) ; that is, 1° 31'. 

It is a curious fact that the line of equinoxes of the moon constantly 
coincides with the line of nodes of its orbit, the ascending node of its 
orbit being situated at the descending node of its equator. Hence the 
lunar equinoxes retrograde with the nodes, and the pole of the moon 
revolves around that of the ecliptic, requiring 18? years to complete 
the circuit. 

Fig. 80. Fig. 80 represents 

P o the moon in two po- 

sitions of her orbit, 
0; at 1, in the 
ascending node, and 
at 2, when she has 
her greatest north- 
ern latitude. E E 
represents the plane 
of the ecliptic, and 
W E', a plane paral- 
lel to it, each pass- 
ing between the 
planes of the moon's equator and orbit, and at the point where the former 
descends below the latter. The angular distance between the planes E E 
and E' E', of course, never exceeds 5^°, which is about .ten times the appar- 
ent diameter of the moon as seen from the earth. Hence, the greatest 
distance between these planes is about ten times the diameter of the moon, 
or 21,600 miles, which at the distance of the sun subtends an angle of 
about 49", and to this extent may affect the inclination of the axis to the 
ecliptic. 

174. Owing to the small inclination of the moon's axis 
to the plane of the ecliptic (1° 31'), she can have but very- 
little change of seasons, and that not constant, because her 
axis does not always point in the same direction. 

a. From what has been said above (Art. 173, d), it will be evident 

Qttestions. — d. Explain and illustrate the position of the lunar axis. What curious 
fact is mentioned ? 174. What change of seasons has the moon ? a. What change m 
the equinoxes and solstices? 




THE MOON. 123 

that the lunar solstices and equinoxes change places with each other 
every 9^ years ; whereas, the period required for a similar change in 
the earth, occasioned by precession, is about 13,000 years. 

175. A lunar day must be nearly 15 times as long as one 
of our days, and a lunar night of the same length ; since 
any place on the moon's surface requires 29 ^ days to return 
to the same relative position with the sun. Hence the sun 
must remain above the horizon during one half of that 
period, and below it the other half. 

a. Mountains situated at either of the lunar poles must have per- 
petual day ; for the sun there can never be more than \\° below the 
horizon ; and on so small a body as the moon, the horizon would dip 
that amount at an elevation of about \ mile. 

b. The Earth's Light. — On one hemisphere of the moon, the long 
night must be relieved by the light of the earth, which exhibits the 
same phases to the moon as the latter does to the earth, except that 
they are reversed ; that is, when the moon is new to us, the earth is 
full to the moon ; and when the lunar form is but a slender crescent, 
the earth is gibbous, showing itself with almost full splendor. Now, 
as the earth's disc contains about 14 times as much surface as that of 
the moon, the light of the earth must cause a very considerable illu- 
mination. 

c. The effect of this is seen when the moon is just emerging from 
conjunction, the dark part of her disc being slightly illumined by the 
light of the nearly full earth, so that the full, round form of the 
moon's disc becomes visible, the bright crescent appearing at the edge 
toward the sun. This is sometimes called " the old moon in the new 
moon's arms." 

d. The Earth appears Stationary to the Moon.— The earth, 
although it exhibits phases to the moon, does not appear to revolve 
around it, but remains at every place on the lunar hemisphere which 
is turned toward it, nearly at a fixed point in the heavens ; this point 
varying, of course, with the change of place of the observer. This 
will be obvious, when it is considered that the rotation of the moon 
would give the earth an apparent motion from east to west; but the 

Questions.— 175. What is the length of a lunar day and night? a. Where is there 
perpetual day ? h. The ear th's light — effect on the moon? c. " The old moon in the 
new moon's arms?"' d. Why must the earth appear stationary to the moon? 



124 THE MOON. 

motion of the moon in her orbit would give it an apparent motion at 
the same rate, from west to east ; hence, one counteracts the other, and 
the earth appears to be almost stationary, only shifting its position 
backward and forward by the amount of libration. 

176. Appearances indicate that the moon has very little, 
if any, atmosphere ; and that its surface is as devoid of 
water as of air. 

a. When viewed with a telescope, the surface of the moon appears 
entirely unobscured by any clouds or vapors floating over it ; and 
when the moon's edge comes in contact with a star, the latter is im- 
mediately extinguished ; whereas, if there were an atmosphere, it 
would, from the effect of refraction, rest on the edge for a short time ; 
that is, it would be visible when a short distance actually behind the 
moon. Observations of this kind have been made with so much 
nicety, that it is believed that an atmosphere two thousand times less 
dense than that of the earth could not have escaped detection. If any 
atmosphere therefore exists, it must be rarer than the attenuated air 
in the exhausted receiver of the most perfect air-pump. 

b. The absence of water follows from that of air ; since, without 
the latter, the heat of the sun would be incapable of preserving the 
temperature above the freezing point ; as we see on the tops of terres- 
trial mountains, which are constantly covered with snow, from the 
extreme rarefaction of the air at those heights. If water existed, it 
would therefore soon be converted into ice ; but we see no indications 
of it even in this form. 

c. Some have accounted for this by supposing that the internal heat 
of the moon was once very great, as is that of the earth at the present 
time ; but that having cooled, the moon has contracted in volume, and 
that vast caverns have thus been formed in its interior, into which the 
water has penetrated, and, of course, disappeared. Indeed, it is obvi- 
ous that only great internal heat could keep an ocean upon the surface 
of a body like the earth or moon. 

SELENOGRAPHY. 

177. That part of the moon's surface which is turned 
toward the earth has been very carefully observed, and all 

Questions.— 176. Has the moon any atmosphere? a. How is this known? b. Why 
no water? c. How accounted for ? 177. What is selenography ? 




THE MOOK. 



125 



the objects upon it delineated upon maps or charts, so as to 
show their exact forms and relative positions. This branch 
of astronomical science is called Selenogkaphy.* 

a. This department of the astronomer's labors has been prosecuted 
with extraordinary zeal and industry by the Prussian astronomers, 
Beer and Madler. Their chart, measuring 37 inches in diameter, 
exhibits the lunar surface with the most astonishing minuteness and 
accuracy. Other charts have also been constructed ; and the moon is 
still receiving a very scrutinizing survey by a number of eminent 
astronomers, each taking a separate belt or zone, with the object of 
arriving at still greater minuteness of delineation. 

178. The moon's disc when viewed through a telescope 
presents a diversified appearance of dusky and bright spots ; 
the latter being evidently elevated portions of the surface, 
and the former, plains or valleys. 

a. The dusky patches were once thought to be seas, and they still 
Fie:. 81. 




PHOTOGRAPHIC VIEWS OF THE MOON. — De Ld Rue. 

* From the Greek word selene, the moon, and graphy, a description. 

Questions. — a. Construction of lunar charts? 178. How does the moon appear 
when viewed through a telescope ? a. What are the dusky patches ? 



126 



THE M002>T. 



retain these names in selenography, although without any such literal 
meaning ; thus, one is called Mare Tranquillitaiis, or Sea of Tranquil- 
lity ; another, Mare JSfectaris, Sea of Nectar, etc. 

b. Lunar Mountains. — Mountains on the moon's surface are indi- 
cated by the bright spots that appear scattered over the disc, and 
beyond the terminator, or line that separates the dark from the illumi- 
nated part of the disc, and by the shadows cast upon the surface of the 
moon when the sun shines obliquely upon these elevations. 

c. These mountains are of various forms, including with others, the 
following : — 

1. Bugged and precipitous ranges, many of a circular form, enclos- 
ing great plains, called on this account, " Bulwark Plains," from 40 to 

Fig. 82. 




OOPEKNICTJ8, FEOM A DRAWING BY SIE JOHN HEESCHEI,. 

120 miles in diameter ; 2. Lofty mountains, of a circular form, 
enclosing an area from 10 to 60 miles in diameter, resembling the crater 



Questions. — b. How are mountains indicated ? c. What classes of mountain for- 
mations ? 



THE MOON. 



127 



of a volcano but of vast size, and sometimes containing in the centre one 
or more lofty peaks : such formations are called Ring Mountains; 
3. Smaller cavities, called craters, also enclosing a visible space, and a 
central mound ; and 4. Deep hollows, called holes, showing no enclosed 



From the Ring Mountains, streaks of light and shade radiate on all 
sides, spreading to a distance of several hundred miles. These are 
called radiating streaks. They are attributed by some to the streams 
of lava which once flowed in all directions from these evidently vol- 
canic mountains. 

d. Copernicus. — (Fig. 82) — This is one of the grandest of the 
Ring Mountains. It is 56 miles in diameter, and has a central 
mountain, two of whose six peaks are quite conspicuous. The 
summit, a narrow ridge, nearly circular, rises 11,000 feet above the 
bottom. It is very brilliant in the full moon, sometimes resembling a 
string of pearls. It lies on the terminator a day or two after first 
quarter. Another of the Ring Mountains (Tycho) is visible to the 
naked eye, in the southeast quadrant of the moon. It is 54 miles 
across, and is 1 6,600 feet high. 



Beer and Madler have calcu- 
Fig. 83. 



e. Height of Lunar Mountains 
lated the height of more than 1000 
mountains, several of which reach 
an elevation of 23,000 feet, which 
is nearly equal to that of the loftiest 
terrestrial peaks; and, of course, 
relatively very much greater. 

To understand the principle on 
which the altitude of the lunar mount- 
ains is found, let E (Fig. 83) repre- 
sent the position of the earth, C, the 
centre of the moon, S, the direc- 
tion of a ray of the sun, falling on the 
top of a mountain at M, which there- 
fore appears to an observer at E, at 
the distance A M from the terminator 
at A. Now, this distance can be found 
by angular measurement and calcula- 
tion. Suppose it to be about & of the apparent diameter of the disc, or 




Questions. — d. Describe Copernicus, e. Height of lunar mountains ? How found V 



128 THE MOON. 

about V\ then A M will be is of the moon's diameter, or about 72 miles. 
Then, from the properties of the right-angled triangle, (A C) 2 + (A M)* = 
(C M)2 ; that is, (1080)2 + (72)2 = ( C M ) 2 = 1,171,534 ; the square root of which, 
1082.4, will be C M. As this is the siim of the moon's radius and the 
height of the mountain, the latter must be 1082.4 — 1080 = 2.4 miles. 

/. The General Physical Condition of the Moon's Surface, 
therefore, as far as we can observe it, is characterized by uniform deso- 
lation and sterility. Sir John Herscliel says, that among the lunar 
mountains is seen in its greatest perfection, the true volcanic charac- 
ter, as observed in the crater of Mt. Vesuvius and elsewhere, except 
that the internal depth of these lunar craters is sometimes two or 
three times as great as the external height, and that they are of vastly 
greater magnitude; By means of the great telescope of Lord Rosse, 
the interior of some of these craters is seen to he strewed with huge 
blocks, and the exterior crossed by deep gullies radiating from the 
centre. No reliable indication of any active volcano has ever been 
obtained ; although, Sir William Herschel, in 1787, asserted that he 
had seen three lunar volcanoes in actual operation. 

g. Are there People in the Moon ? — This question has often been 
discussed, but idly ; since no positive evidence can be adduced on one 
side or the other. The distance of the moon is too great for us to 
detect any artificial structures, as buildings, walls, roads, etc., if there 
were any ; and certainly, without air or water, no animals such as 
inhabit our own planet could exist there. But the Almighty Creator 
can place animals and intelligent beings in any part of the universe, 
and accommodate them to the peculiar circumstances of their abode ; 
and it would perhaps be strange if He had left even our little satel- 
lite without an intelligent witness of His infinite power and benefi- 
cence. 

IRREGULARITIES OF THE MOON'S MOTIONS. 

179. The attraction of the sun acting unequally on the 
moon in different parts of its orbit gives rise to very many 
disturbances and irregularities in its motion ; so that it is a 
very difficult problem to calculate its exact place at any 
given time. 

Questions.—/. Physical condition of the moon's surface ? g. Is the moon inhabited ? 
179. Lunar irregularities — how caused ? 



THE MOOX. 129 

a. The sun's attracting force upon the moon acts directly in con- 
junction and opposition, but, on account of the difference in the 
distance, is greater in the former position than in the latter ; while at 
the quadratures, it acts obliquely, thus giving rise to a variety of dis- 
turbances, or perturbations. 

b. The attraction of the sun upon the moon is absolutely more than 
twice as great as that of the earth ; but being very nearly equal 
on both earth and moon, they move with regard to each other 
almost as if they were not attracted at all by the sun. If the attrac- 
tion of the sun upon the earth were suspended, the moon would 
abandon the earth, and either revolve around the sun, or move directly 
to it. As the distance of the earth and moon from each other is so 
small relatively to their distance from the sun (about - 3 -i 4 ), their mutual 
attractions are not much disturbed by the action of the sun ; but they 
are to some extent. Thus, in conjunction, the moon is attracted more 
than the earth, but in opposition, less ; so that the tendency of the 
sun's force is to pull them apart when in either of these positions. In 
the quadratures, however, the sun's force acts obliquely, and con- 
sequently tends to pull them together. Hence, we may say, the 
attraction of the earth upon the moon is diminished in the syzygies, 
and increased in the quadratures. 

c. The following are the principal irregularities or inequalities to 
which the moon's motion is subject : (Those completed in short periods 
are called periodical ; those" that require very long periods for their 
completion are called secular?) 

1. Evection, which is the largest of these inequalities, is the variation 
in the moon's longitude, due to the action of the sun, above referred to. 
It depends upon the moon's angular distance from the sun, and the 
eccentricity of its orbit. By it the equation of the centre of the moon 
is diminished in syzygies and increased in quadratures. It may influ- 
ence the moon's longitude to the extent of 1° 20'. This irregularity 
was discovered by Ptolemy. 

2. The variation, which also affects the longitude of the moon to 
the extent of 30'. It arises from the disturbing force of the sun, act- 
ing upon the moon when in the octants, or points half-way between 
the syzygies and quadratures. This was discovered by Tycho Brahe, 

Questions.— «. How does the sun's force act ? 6. Its effect in syzygies and quadra- 
tures ? c. What is evection ? The variation ? 



130 THE MOON. 

and was the first lunar inequality explained by Sir Isaac Newton by 
applying the law of gravitation. 

3. The annual equation, which results from the varying velocity of 
the earth in its orbit. It may affect the moon's longitude about 11'. 

4. The 'parallactic inequality, arising from variations in the disturb- 
ing force of the sun upon the moon according as the latter is in that 
part of its orbit nearest to, or farthest from, the sun. It may affect the 
moon's longitude to the extent of 2'. 

5. The secular acceleration of the moon's mean motion, caused by 
the diminution of the eccentricity of the earth's orbit. At present it 
amounts to 10" every 100 years, the periodic time of the moon being 
constantly diminished to that extent. This was discovered by Halley 
in 1693, by comparing the periodic time of the moon, as deduced from 
Chaldean observations of eclipses made at Babylon, 720 and 719 B.C., 
with Arabian observations made in the 8th and 9th centuries A.D. 
La Place demonstrated its cause. At a very distant period, this 
inequality will, of course, be reversed, becoming a retardation instead 
of an acceleration. 

d. Other irregularities have been discovered, caused by the disturb- 
ing action of Venus. These various inequalities constitute what is 
called the Lunar Theory ; and when they are all applied, the computed 
place of the moon should precisely agree with the observed place. 

Questions. — The annual equation ? The parallactic inequality ? The secular accele- 
ration 1 d. What other inequalities ? The Lunar Theory ? 



CHAPTER X 



ECLIPSES. 

180. An Eclipse* is the concealment or obscuration of 
the disc of the sun or moon by an interception of the sun's 
rays. Eclipses are, therefore, either Solar or Lunar. 

181. A Solar Eclipse is caused by the passage of the 
moon between the earth and sun so as to conceal the sun 
from our view. 

182. A Lunar Eclipse is caused by the passage of the 
moon through the earth's shadow. 

a. By a shadow is meant simply the space from which the light of a 
luminous body is wholly intercepted by the interposition of some 
opaque body. Since light proceeds from a luminous body in straight 
lines, and in all directions, the darkened space formed behind the 
earth or moon must be conical ; that is, of the form of a cone, circular 
at the base and terminating at a point ; since the sun or luminous 
body is larger than either of the opaque bodies. The shadow is some- 
times called by its Latin name, umbra. 

b. Besides the totally darkened space called the umbra, there is 
formed on each side a space from which the light is only partially 
excluded ; this is called the penumbra.\ The relations of the umbra 



* From the Greek word ekleipsis, which means a, fainting away. The ecliptic 
is so called because eclipses only take place when the moon is in its plane, 
t From the Latin word pene, meaning almost, and umbra, meaning a 
shadow. 

Questions.^— 180. What is an eclipse ? Of how many kinds ? 181. How is a solar 
eclipse caused? 182, A lunar eclipse? a. How is a shadow defined? The form of 
the earth's or moon's shadow? b. Define the terms umbra and penumbra. 



182 



ECLIPSES, 



to the penumbra will be understood by inspecting the annexed dia- 
gram (Fig. 84). 

Pig. 84. 




SOLAB AND LUNAE ECLIPSES. 



183. If the moon moved exactly in the plane of the 
earth's orbit, a solar eclipse would occur at every new moon, 
and a lunar eclipse at every full moon ; but as the moon's 
orbit is inclined to that of the earth, an eclipse can only 
happen when the moon is at or near one of its nodes. 

a. When the moon is new or full at a considerable distance from 
its node, it is too far above or too far below the plane of the ecliptic to 
intercept the sun's rays from the earth, or to pass within the limits of 
the earth's shadow. It will be easily understood that no eclipse can 
occur unless the sun, earth, and moon are situated exactly or nearly 
in the same straight line. [See Fig. 84.] 

b. The limit north or south of the ecliptic within which an eclipse 
must occur is larger in the case of solar than in the case of lunar 
eclipses. In the former it varies from 1° 35' to 1° 24' , in the latter, 
from 63' to 52'. 

Questions. — 183. Where must the moon be when an eclipse occurs ? a. How ex- 
plained ? b. What is the limit in latitude for solar and lunar eclipses ? Explain and 
demonstrate each by Fig. 85. 




ECLIPSES 133 

Pig. 85. 




To explain how this is found, let S be the centre of the snn, and O the 
centre of the earth, SOE being the plane of the ecliptic ; let also P be 
the position of the moon at the limit for a solar eclipse, and V, its position 
for a lunar eclipse. The angular distance of the moon's centre from the 
ecliptic in each case is the limit required ; SOmis that angle for the for- 
mer, and nOE, for the latter. Now, SOmis equal toSOB+POmf 
BOP; and S O B is the apparent semi-diameter of the sun, and P O m is 
that of the moon. But, O P C, being exterior to the triangle B O P, is 
equal to the sum of the two interior angles O B P and BOP, and hence 
B O P is equal to OPC-OBC, or the moon's horizontal parallax 
minus that of the sun. Therefore, the solar limit in latitude is equal to the 
sum of the apparent semi-diameters of the sun and moon increased by the differ- 
ence between the horizontal parallax of each ; or 161' + 161' +1° 2' = 1° 35', when 
greatest (omitting the sun's parallax, which is very small); and 15'' -f 14f 
+ 53J' - 1° 24', when least. Hence, when the moon's latitude at the time 
of inferior conjunction does not exceed the former, an eclipse may occur; 
when it does not exceed the latter, an eclipse must occur. 

The angle of limit for a lunar eclipse is n O E, obviously less than S Om. 
It is composed of the angle n O V, or the apparent semi-diameter of the 
moon, and the angle V O E, or the angle subtended by one-half of the 
diameter of the shadow, where the moon traverses it. Now, V O E = O V D 
-OEV, and OEV=AOS-OAD; hence VOE=OVD+OAD 
— A O S. But O V D is the moon's horizontal parallax, O A D is that of 
the sun, and A O S is the sun's apparent semi-diameter. Consequently, 
n E, or the lunar limit in latitude, is equal to the sum of the horizontal 
parallax of the sun and moon, diminished by the sun's apparent semi-diameter, 
and increased by that of the moon. That is, 62' — 15f' + 161' = 63', when 
greatest ; and 53^' — 16|' +141' = 52', when least. These calculations, being 
made only for illustration, are but approximatively correct. 

184. The distance in longitude, either side of the node, 

Question. — 184. What is meant by the ecliptic limit? 



134: 



ECLIPSES. 



Fig. 88. 



within which an eclipse can occur, is called the Ecliptic 
Limit. 

185. The solar ecliptic limit extends about 17° on each 
side of the node ; the lunar ecliptic limit, about 12°. 

a. This difference follows from the difference in the limits in lati- 
tude, the ecliptic limits in longitude being computed from those in 
latitude. 

For in Fig. 86, let B N be 
a portion of the ecliptic, 
A N, a part of the moon's 
orbit, N, the node, A B, the 
solar limit in latitude and 
C D, the lunar. It will be 
at once apparent that since 
A B is greater than C D, it 
must be farther from the node. To calculate the exact amount, there are 
given, in the right-angled triangle A N B, the angle at N = 5*° ; the side 
ABorC D, and the right angle at B, to find the side B N or D N, which 
can easily be done by the higher mathematics. 

b. Since the limits in latitude vary, those in longitude also vary, 
the amount given above being the mean. The greatest solar ecliptic 
limit is 18° 36' ; and the least, 15° 20' ; the greatest lunar ecliptic limit 
is 12° 24' ; and the least, 9° 23'. Within the former, an eclipse may 
happen ; within the latter, it must. 

Fig. 87. 




» m m ** 



mmm-m 



PATH OF THE SUN CROSSED BY THAT OF THE MOON. 

Fig. 87 illustrates the relative position of the sun and moon's orbits, 
with respect to the ecliptic limits. In the centre the moon is exactly at the 
ascending node ; while at the extremes, it is at the limits both in latitude 
and longitude. Except at the node, the moon, it will be apparent, only 
partially covers the disc of the sun, within the limits on each side. 



Questions.— 185. What is the extent of the solar and lunar ecliptic limits? 
do they differ ? b. Why is each not always the same ? 



Why 



ECLIPSES. 135 

186. Since the solar ecliptic limits are wider than the 
lunar, eclipses of the sun are more frequent than those of 
the moon. 

187. The greatest number of eclipses that can happen in 
a year is seven ; five of the sun and two of the moon, or four 
of the sun and three of the moon. The least member is 
two, both of which must be of the sun. 

a. The usual number is four, and it is rare to have more than six. 
From the above statement, it will be seen that the greatest number of 
solar eclipses is five, and the least two ; and that the greatest number 
of lunar eclipses is three, while none at all may occur during the year. 

b. Number of Solar Eclipses. — Since the sun crosses the line of 
nodes twice each year, and his monthly progress in the ecliptic is about 
29°, while a solar eclipse must occur if the moon is within 15° 20' of 
either node, or within a space of 30° 40', there must evidently be a 
solar eclipse each time the sun passes the node, or twice each year. 
Now, if the sun, at the time of new moon is 18° west of the node, it 
may be eclipsed (Art. 185, b) ; and if it were, there would be another 
eclipse at the next new moon, for the sun would have advanced less 
than 11° east of the node. Again, in six lunations from the first new 
moon referred to, the sun would have advanced 174°, and consequently 
would be 174° — 18°, or 156° east of one node, and 24° west of the 
other ; but the node is itself moving to the west about 1%° every luna- 
tion ; and hence, the sun would be only 24° — 9°, or 15°, from the 
node, so that a third eclipse would take place ; and after another 
lunation, a fourth, since the sun would then be less than 15° from the 
node. Now, owing to the retrogradation of the nodes, the sun passes 
from one to the same again in 346 days ; and hence, if it passed one at 
the beginning of the year, it would pass it again toward the end of 
the year, and there would be three passages of a node in that time ; 
so that if four eclipses had previously taken place, there might be still 
another toward the end of the year, making five in all. 

c. Number of Lunar Eclipses. — As the space on each side of the 
node, within which a lunar eclipse must occur, is only about 9^°, or 19° 



Questions. — 186. What eclipses are more frequent? Why? 1ST. What is the 
greatest number of eclipses in a year? The least? a; The usual number? How 
many solar eclipses may happen ? Lunar eclipses? b. How is this proved in respect 
to solar eclipses ? c. Lunar eclipses ? 



136 ECLIPSES. 

on both sides, it is obvious that there might be no lunar eclipse during 
the year ; but, since an eclipse may occur within a space of 25° (12° 24' 
on each side of the node), it follows that one lunar eclipse may oceu» 
at each passage of the sun, or three during the year. But three lunar 
eclipses can not be preceded by five solar eclipses in the same year ; for 
two solar eclipses can not take place at one node, unless, at the first one, 
the sun is at least about 10° west of the node, so that there would not 
be enough space at the end of the year for both a solar and a lunar 
eclipse. 

188. Solar eclipses do not actually occur as often as lunar 
eclipses at any particular place ; because the latter are always 
visible to an entire hemisphere, whereas the former are only 
visible to that part of the earth's surface covered by the 
moon's shadow or its penumbra. 

a. That the moon, in a lunar eclipse, is concealed from an entire 
hemisphere, will be obvious from the fact that the diameter of the 
earth's shadow where the moon crosses it is always more than twice as 
great as the diameter of the moon, and is sometimes nearly three times 
as great. For the angle VOW (Fig. 85) is equal to the sum of the hori- 
zontal parallax of the sun and moon, diminished by the apparent semi- 
diameter of the sun (183, b). The greatest parallax of the moon is about 
62', and the least, 53^' ; and the least apparent semi-diameter of the 
the sun is 15 1', and the greatest, 16 \' ; hence, the angle V W is, 
when greatest, 44^' (omitting the sun's parallax) ; and when least, S7\' ; 
the mean being about 40 f. As this is the angular value of the semi- 
diameter of the shadow, it must be doubled for the whole, which 
therefore is, when greatest, 88" ; least, 74^' ; mean, 81i'. Hence, 
as the moon's apparent diameter is, when greatest, 33 ¥ ; least, 29^' ; 
mean, 31£', the truth of the above statement will be apparent. 

b. Length of the Earth's Shadow. — This can be readily found by 
comparing the triangles A S E and DEO (Fig. 85), which being both 
right-angled triangles, and having all their angles respectively 
equal, have, by a principle of geometry, proportional sides ; so that 
A S : D O : : S E : O E. But D O, the semi-diameter of the earth, is about 
tot of AS, the semi-diameter of the sun; hence OE, the length of 

Questions. — 188. What eclipses are the more frequent at any place ? Why ? a. 
Why is the moon concealed from an entire hemisphere ? b. What is the length of the 
earth's shadow ? How demonstrated ? 



ECLIPSES. 



137 



th« shadow, must be rfo of S E ; and therefore, S must be \%$ of the 
whole distance S E, and, of course, S E, {$% of S O ; but O E, the 
length of the shadow, is equal to S E— S ; hence it is equal to yfo of 
S O, or the distance of the earth from the sun. Therefore its greatest 
length is about 877,000 miles, and its least, 850,000 miles ; that is, at 
its mean length, a little more than the diameter of the sun. 

Fig. 88. 




c. Length of the Moon's Shadow.— This can be found by a similar 
calculation. Let S (Fig. 88) be the centre of the sun, and O, that of the 
moon ; P will then be the end of the shadow, and O P its length ; and, 
in the triangles A S P and O M P, A S :MO :: SP : OP. Now, MO is 
about 3i T of A S ; hence O P is th of S P, and S O, ||| of S P ; or S P, 
||$ of S O ; therefore O P is ^ of S O, the distance of the moon from the 
sun. Now, the moon's distance from the earth varies between 252,000 
miles and 226,000 miles ; and the earth's distance from the sun, 
between 93 millions and 90 millions ; hence, at the mean distance of 
the earth and moon, the length of the shadow is about 232,000 miles, 
or 6,000 miles from the earth's centre, and 2,000 miles from its surface. 
When the earth is in aphelion and the moon in perigee, it extends 
about 10,000 miles beyond the earth's centre, or 14,000 miles from the 
surface a b, which is the maximum. When the earth is in perihelion 
and the moon in apogee, the shadow is about 228,000 miles long, 
while the moon is 252,000 miles from the earth's centre ; so that it 
fails to reach the surface of the earth by 20,000 miles. 

d. Breadth of the Moon's Shadow. — When the end of the 
shadow extends to the greatest distance beyond the earth's centre, the 
amount of surface covered by it is the greatest possible. Let a b (Fig. 
88) be the diameter of the shadow where it intersects the earth : and 



Questions. — e. The length of the moon's shadow? How demonstrated ? d. How 
much of the earth's surface may be obscured by the moon's shadow? How proved? 
How much by the moon's penumbra ? 



138 ECLIPSES. 

since it is a very small arc, we may find its approximate length by con- 
sidering it a straight line. We shall then have, by comparing the 
triangles, A P : a P : : A S : \a b ; but a P is 14,000 miles (183 c), and A P is 
93,014,000 miles. Hence, 93,014,000 : 14,000 : : 426,000 : lab =64miles+. 
Therefore a b, or the breadth of the shadow where it intersects the 
earth is about 128 miles. The breadth of the portion of the earth's 
surface covered by the shadow is, really, 1° 54', or 130 miles. This is the 
maximum. The breadth of the greatest portion of the earth's surface 
ever covered by the moon's penumbra is 70° 17', or 4,850 miles. 

189. When the whole of the sun's or moon's disc is con- 
cealed, the eclipse is said to be total ; when only a part of 
it is concealed, it is said to be partial. 

190. In order to measure the extent of the eclipse, the 
apparent diameters of the sun and moon are divided into 
twelve equal parts, called digits. 

Fig. 89. 




A PAETIAL ECLIPSE OF THE 8UN AND MOON. 

a. The conditions of a total and a partial eclipse will be apparent 
from the explanations already given. When the centres of the sun 
and moon coincide, that is, when the latter is exactly at the node, the 
eclipse is said to be central. A central eclipse of the moon must, of 
course, be total ; but a solar eclipse may be central without being 
total ; since sometimes, as it has been demonstrated, the shadow of the 
moon does not reach the earth. The moon, when this is the case, covers 



Questions.— 189. When is an eclipse total? When partial ? 190. What are digits? 
a. What is a central eclipse ? 



ECLIPSES. 139 

only the central part of the sun's disc, leaving a ring of luminous sur- 
face visible around the opaque body. This is called an annular * 
eclipse. 

191. An annulae eclipse is an eclipse of the sun, which 
happens when the moon is too far from the earth to conceal 
the whole of the sun's disc, leaving a bright ring around the 
dark body of the moon. 

192. The time at which an eclipse will occur may be dis- 
covered by finding the mean longitudes of the sun and node 
at each new or full moon throughout the year, and compar- 
ing the difference of the longitudes with the ecliptic limits. 

Fig. 90. 




AN ANNULAR ECLIPSE. 



a. Cycle of Eclipses. — Eclipses of both the sun and moon recur 
in nearly the same order, and at the same intervals, after the expiration 
of 18 years and 10 or 11 days (according as there may be 5 or 4 leap- 
years in this period). For a lunation is about 29.53 days, and the time 
of a revolution of the sun with respect to the node, 346.62 days, which 
periods are nearly in the ratio of 19 to 223 ; so that 223 lunations are 
almost equal to 19 revolutions of the sun ; and 346.62 days X 19= 18? 
11 j d . This is called the cycle or period of eclipses. The eclipses which 
occur during one such period being noted, subsequent eclipses may 
easily be predicted ; as their order is the same, only they are 10 or 11 
days later in the month, and about eight hours later in the day ; so 



* From the Latin word annulus, meaning a ring. 



Questions. — 191. What is an annular eclipse ? How caused? 192. How to predict an 
eclipse ? a. What is the cycle of eclipses ? How calculated ? How named by the Chaldeans ? 



140 ECLIPSES. 

that in one cycle eclipses may be visible, and in the next invisible, to a 
particular place. During this period there are generally 41 solar and 
29 lunar eclipses. This cycle was known to the ancient Egyptians 
and Chaldeans, and called by them Saws. 

193. The phenomena connected with a total eclipse of the 
sun are of a peculiarly interesting character, and have been 
observed by astronomers with great attention and industry. 

a. To an ignorant mind, this occurrence must be the occasion of 
very great awe, if not actual terror. A universal gloom overspreads 
the face of the earth as the great luminary of day appears to be ex- 
piring in the sky ; the stars and planets become visible, and the animal 
creation give signs of terror at the dismal and alarming aspect of 
nature. Armies about to engage in battle have thrown down their 
arms and fled in dismay from the seeming anger of heaven. This was 
the case at the eclipse predicted by Thales, which occurred on the eve 
of the battle between the Medes and Lydians, 584 B.C. 

b. Phenomena of a Solar Eclipse. — The following are the most 
interesting of the phenomena presented during a total eclipse of the 
sun:— 

1. The change of color in the sky from its ordinary blue or azure 
tinge to a dusky, livid color intermixed with purple. Kepler men- 
tions that during the solar eclipse in 1590, the reapers in Styria noticed 
that every thing had a yellowish tinge. The darkness is not, however, 
total, but sufficiently great to prevent persons' reading. 

2. The corona, or halo of light which appears to surround the moon 
while it covers the disc of the sun. This is, at the present time, sup- 
posed to be caused by the atmosphere of the sun. 

3. When the moon has almost covered the disc of the sun, leaving 
only a line of light at the edge, this line is broken up into small por- 
tions, so as to appear like a band of brilliant points. This phenomenon 
is called Baily's beads, from Mr. Francis Baily, who was the first to 
describe it minutely, in 1836. This is supposed to be caused by the 
irregularities of the moon's surface, serrating its dark edge, and pro- 
jected on the sun's brilliant disc. 

4. Pink or rose-colored protuberances which project from the margin 
of the moon's disc when the obscuration is total. One measured by 

Questions. — 193. The phenomena connected with a total eclipse ? a. Effect on igno- 
rant minds? b. State the most interesting phenomena presented by a solar eclipse ? 
The corona ? Baily 1 s beads ? Rose-colored protuberances ? Explain the cause of each. 




ECLIPSES. 141 

De La Rue, in 1860, was found to be at least 44,000 miles in vertical 
height above the sun's surface. They have been seen by most observ- 
ers. No entirely satisfactory cause has been assigned for these 
appearances, although it seems to be settled that their origin is in 
the sun and not the moon ; and it is thought by some that they are 
clouds floating in the atmosphere of the sun, their peculiar color being 
caused by the absorption of the other colors, as sometimes occurs in 
the case of clouds in our own atmosphere. 

c. Appearance of a Lunar Eclipse.— In a total lunar eclipse, the 
moon does not become wholly invisible, but assumes a dull, reddish 
hue, which arises from the refraction of the sun's rays by the earth's 
atmosphere. The red color is caused by the absorption of the blue 
rays in passing through the atmosphere, just as the western sky as- 
sumes a ruddy hue when illuminated in the evening by the solar light. 
Sometimes, however, it happens that the moon is rendered very nearly 
invisible, as was the case in 1643 and 1816 ; and the degree of distinct- 
ness of the moon's appearance varies considerably at different times, 
owing to the different conditions of the atmosphere. 

d. Earliest Observations of Lunar Eclipses. — These were made 
by the Chaldeans, — the first recorded eclipse having taken place in 720 
B.C. This eclipse was total at Babylon, and occurred about 9£ o'clock 
P.M. The record of the occurrence of eclipses is often very useful in 
fixing the dates of history. 

194. An Occultation is the concealment of a planet or 
star by the interposition of the moon or some other body. 

The occultation of a planet or star by the moon is a very interesting 
and beautiful phenomenon. From new moon to full moon, she 
advances eastward with the dark edge foremost, so that the occulted 
body disappears at the dark edge and re-appears at the enlightened 
edge. In the other part of her orbit this is reversed. The former 
phenomenon is of course the more striking, the star or planet appear- 
ing to be extinguished of itself. 

Questions. — c. Describe the appearance of a lunar eclipse, d. Earliest observations 
—by whom made? 194. What is an occultation ? 



CHAPTER XI 



THE TIDES. 

195. Tides are the alternate rising and falling of the 
water in the ocean, bays, rivers, etc., occurring twice in about 
twenty-five hours. 

196. Flood Tide is the rising of the water, and at its 
highest point is called high water. Ebb Tide is the falling 
of the water, and at its lowest point is called low water. 

197. The tides are caused by the unequal attraction of the 
sun and moon upon the opposite sides of the earth. 

a. Since the attraction of gravitation varies inversely as the square 
of the distance, the sun and moon must attract the water on the side 
nearest to them more than the solid mass of the earth ; while on the 
side farthest from them, the water must be attracted less than the 
solid earth ; hence, there must be a tendency in the water to rise at 
each of these points ; it being drawn away from the earth at the point 
toward the sun or moon, and the earth being drawn away from it at 
the other point. At the points 90° from these, the effect of the attrac- 
tion is just the reverse ; for since it does not act in parallel lines, it 
tends to draw together the two sides of the earth, and thus compresses 
the water so as to cause it to recede, and hence increases its tendency to 
rise at the other points. 

Thus at A (Fig. 91) the water is attracted by the sun more than the 
earth, and at B less ; while at C and D the attraction squeezes in the water, 
as it were, so as to make it recede still more, and thus to augment its rising 
at A and B. It will be obvious that the attraction of the moon acts so as to 
disturb the water just as that of the sun does ; hence, in the position repre- 

Qttestions.— 195. What are tides ? 196. What is flood tide ? Ebbtide? 19T. How 
are the tides caused ? a. How many points of the earth's surface are affected simul- 
taneously ? How is this explained ? 



THE TIDES. 143 

sented in the diagram, when the moon is in opposition, the action of both the 
sun and moon is exerted upon the same points, A, B and C, D ; and it will 
also be obvious that if the moon were in conjunction, that is, on the same 
side of the earth as the sun, the effect would be the same, because the 
6ame points would be acted upon. 

Fig. 91. 




. b. From the above explanation, it will be apparent that similar 
tides must occur simultaneously on opposite sides of the earth ; namely, 
flood tides on the side turned toward and that turned from the sun or 
moon, and ebb tides at the two points 90° distant. 

198. Since the moon is so much nearer to the earth than 
the sun is, its attraction on the opposite sides is much more 
unequal, and consequently its disturbing action is greater. 
At the mean distance of the sun and moon from the earth, 
the disturbing or tidal force of the moon is about 2| times 
that of the sun. 

a. Considering the moon's mean distance from the centre of the 
earth 238,000 miles, and the earth's diameter 8,000 miles, the moon 
must attract the side of the earth nearest to her more than the oppo- 
site side in the ratio of (234,000) 2 to (242,000) 2 ; that is, as 1 to 1.07 
(nearly). Hence, the moon's disturbing force is .07 of her own attrac- 
tion. Taking the sun's mean distance from the earth's centre at 
91,500,000 miles, the ratio of his different attractions will be as 
(91,496,000) 2 to (91,504,000) 2 , or as 1 to 1.000175 (nearly) ; that is, the 
sun's disturbing force is equal to .000175 of his own attraction. 



Questions. — h. What tides occur simultaneously? 198. TTow does the moon's tidal 
force compare with the sun's ? or. By what calculation is this proved ? 



144 THE TIDES. 

Now, the mass of the sun is about 25,200,000 times that of the moon 

25,200,000 
[315,000 X 80], and its distance, 385 times as great ; hence, — Togi^" - = 

170 (nearly) will be the force of the sun upon the earth, the moon's 
being 1 ; in other words, the sun's attraction on the earth is to the 
moon's as 170 to 1. Hence, 170 X .000175, which is equal to .02975, is 
the sun's disturbing force, while the moon's, as above shown, is .07 ; 
and therefore the former is to the latter as .02975 to .07, or as 1 to 2£. 
This calculation being designed merely to illustrate the principle, is 
made with only approximate accuracy, but gives the true result as 
found by the higher mathematics. Sir Isaac Newton computed this 
ratio as 23 to 58, or 1 to 2£, by calculations based upon the observed 
differences of the height of spring and neap tides. 

b. In the above calculation, the moon's mass is supposed to be 
known, and is made use of to determine the relative forces of the sun 
and moon ; but, practically, the problem is reversed, the comparative 
disturbance of the two bodies being deduced by observations of the 
tides themselves, and then employed to determine the moon's mass. 

199. "When the sun and moon are on the same or oppo- 
site sides of the earth, they unite their attractions, and thus 
raise the highest flood tides at the points under or opposite 
them and the lowest ebb tides at the points 90° from these. 
Such tides are called spring tides ; and they occur at every 
new and full moon, or a short time afterward. 

200. When the moon is in quadrature, its tidal force is 
partly counteracted by that of the sun, since the two 
forces act at right angles with each other; and conse- 
quently the water neither rises so high at flood, nor descends 
so low at ebb tide. Such tides are called neap tides ; they 
occur when the moon is in either of the quarters. 

Fig. 92 represents neap tide. The effect of the sun at A and B, and of 
the moon at C and D, is to equalize the height of the water all over the 
earth. The pupil must understand in inspecting these diagrams, that the 
actual effect of the sun or moon is not, by any means, so great as is repre- 

Qttestions. — b. Practically, is this computed from the moon's mass? 199. What are 
spring tides ? How caused ? 200. What are neap tides ? How caused ? When do 
spring and neap tides occur ? 



THE TIDES. 145 

sentecL It is, in fact, but a few feet, while the earth's diameter is nearly 
8,000 miles. 

Pig. 92. 




a. Since the tidal force of the moon is so much greater than that of 
the sun, it is the passage of the former across the meridian that deter- 
mines the rising of the tide at any place, this lunar tide being either 
augmented or diminished by the inferior tidal force of the sun. 

b. The tides not only vary according to the position of the moon 
with regard to the sun, but are sensibly affected by the variations in 
the distance of the moon from the earth, increasing and diminishing 
inversely with it, but in a more rapid ratio. 

c. The height of the spring tides is to that of the neap tides, gen- 
erally, as 2\ to 1. For spring tide is the result of the sum of the 
moon and sun's forces, or 2^ -f- 1 = 3j ; and neap tide, the result of 
the difference, or 2£ — 1 = 1£ ; and 3$- : 1£- : : 2£ : 1. This varies at 
different places ; at Brest, in France, the spring tides rise to the height 
of over 19 feet, and the neap tides about 9 feet. On the Atlantic coast 
of the United States, the height of the former is to that of the latter 
as 3 to 2. 

d. In the northern hemisphere, the highest tides occur during the 
day in summer, and during the night in winter ; but in the southern 
hemisphere this is reversed. 

This will be apparent from an inspection of Fig. 91. The greatest tidal 

Questions. — a. What determines the rising of the tide at any place? b. "What 
additional cause of variation in the tides ? c. How does the height of spring tides 
compare with that of neap tides ? d. What difference between the diurnal and noctur- 
nal tides ? Why ? 



146 THE TIDES. 

elevation of the water is of course at A and B, and diminishes north and 
south of these points. At a the elevation of the water is obviously greater 
than at 6 ; hut a is the position of a place in the northern hemisphere, at 
noon, and in summer, since the axis is turned toward the sun, and 6, its 
position at midnight ; so that the tide is higher during the day than during 
the night, in this season. Conceive the axis turned the other way, and it 
will he at once seen that the reverse is true in winter. 

e. The height of the tide, therefore, varies with the declinations of 
the sun and moon, being greater in proportion as the two bodies are 
near the equator. If at the time of the equinoxes the moon happens to 
be near the equator, the tides are the highest of all, and are called the 
Equinoctial Spring Tides. 

201. The tides do not rise at the same hour every day, but 
generally about 50 minutes later; because, as the moon 
advances in her orbit, the same place on the earth's surface 
does not come again under the moon until about 50 min- 
utes later than on the previous day. 

a. The interval which elapses from the moon's passing the merid- 
ian of a place until it returns to the same again is 24 h 50 m 28 s ; the 
interval, therefore, between two successive tides is 12 b 25 m 14*. This 
is not, however, always the true interval, from circumstances which 
will be explained hereafter. 

202. The tide does not generally rise until two or three 
hours after the moon has passed the meridian ; because, on 
account of its inertia, the water does not immediately yield 
to the action of the sun or moon. 

a. By inertia is meant the resistance which matter of every kind 
makes to a change of state, whether of rest or motion ; that is, it can not 
put itself in motion, neither can it stop itself. The tides are not only 
retarded by inertia, but, to some extent, by the friction on the bed of 
the ocean or the sea, or the sides of rivers and confined channels. 

b. Solar and Lunar Tide Waves. — The solar tide wave is more 
retarded than the lunar, since the tidal force of the sun is so much 

Questions.— e. Equinoctial spring tides ? 201. Why do the tides rise later from day 
to day? 202. Why are the tides hehind the moon ? a. Inertia ? 6. Which tide waves 
are more retarded, the solar or lunar ? What is meant by the priming and lagging of 
the tides ? 



THE TIDES. 147 

feebler than that of the moon. The general retardation of the tides 
depends on the relative position of the solar and lunar tide waves. At 
new and full moon the solar tide wave, being more retarded, is east of 
the lunar ; and, therefore, high water, which results from the union of 
the two waves, must be east of the place it would have been if the 
moon had acted alone ; and hence, on this account, the tide will rise 
later. When, however, the moon is in either of the quarters, the 
solar tide wave is west of the lunar, and the tide rises earlier. This is 
called the priming and lagging of the tides ; since it either shortens or 
lengthens the tidal day of 24 h 50 m 28 g . The highest spring tide rises 
when the moon passes the meridian about l£ h after the sun ; for then 
the two tide waves immediately coincide, 

c. These tide waves are not to be conceived as currents moving pro- 
gressively through the ocean, but as undulations rising nearly under 
the sun and moon, and, as the earth turns on its axis, moving westward 
over its surface, at the same rate. This would be the case exactly, and 
at all parts of the earth, if it were uniformly covered with water, so 
that the great tide wave could move without any obstruction from oppos- 
ing shores. In the open ocean it constantly follows the moon at the 
distance of about 30° from her ; but the tide rises at every place at a 
different time owing to the peculiarities of its situation. Lines drawn 
on the map or globe through all the adjacent places which have high 
water at the same time, are called cotidal lines. 

d. The average interval of time between noon and the time of high 
water at any port on the days of new and full moon, is called the 
establishment of the port. The mean establishment of New York is 
about 81 hours ; of Boston, 11£ hours ; of San Francisco, 12^ hours. 

203. The tides that occur in rivers, narrow bays, or other 
bodies of water at a distance from the ocean, are not caused 
by the immediate action of the sun and moon, but arise from 
the undulations of the great ocean tide wave, urging the 
water into these contracted inlets. The tides of the ocean 
are called primitive tides ; those of rivers, inlets, etc., are 
called derivative tides. 



Qttesttons.— c. Do the tides rise at the same time at all places? WBynot? 203. 
What are primitive tides ? Derivative tides ? 



148 THE TIDES. 

204. The average height of the tide for the whole globe is 
about 2^ feet ; and this is the height to which it rises in the 
ocean. The height, however, at any particular place de- 
pends upon its situation; the highest tides occurring in 
narrow bays, and arms of the sea running up into the land. 
Lakes have no perceptible tides. 

a. The highest tides in the world take place in the Bay of Fundy, 
the mouth of which is exposed to the great Atlantic tide wave. At 
the head of the bay the ordinary spring tides rise to the height of 50 
feet, while special tides have been known to rise as high as 70 feet. 
In New York, the height of the tide is, at its maximum, about 8 feet ; 
in Boston, 11 feet. On the other hand, at some places there is scarcely 
any tide at all. An instance of this is found at a point on the south- 
eastern coast of Ireland, the tide stream being diverted to the opposite 
shore by a promontory at the entrance of St. George's Channel. 

b. Velocity of the Tide- Wave. — This is affected by various cir- 
cumstances ; such as the depth of the water, the obstructions from 
opposing shores, etc. The moon tends to draw the water along with 
it at the rate of 1,000 miles an hour at the equator ; but the actual 
rate of movement is much less rapid. The tide wave requires about 
40 hours to reach the Atlantic coast from the south-eastern Pacific, 
where it originates, traversing the Pacific, Indian, and South Atlantic 
oceans. When it strikes the shallow waters of the coast its velocity is 
greatly diminished, not exceeding, sometimes, 50 miles an hour. Its 
breadth is, of course, diminished with its velocity. At a velocity of 
600 miles an hour, its breadth would be over 7,000 miles ; but when 
the velocity is reduced to 100 miles an hour, its breadth is only about 
1200 miles. 

c. Atmospheric Tides. — The same causes that act to disturb the 
ocean must also produce similar disturbances in the atmosphere. The 
atmospheric tides, however, have been demonstrated by Laplace to 
be very inconsiderable in height, not exceeding, at Paris, one-thou- 
sandth of an inch, — an amount far too small to be indicated by 
ordinary observations with the barometer. 

Questions.— 204. What is the average height of the water for the whole globe ? On 
what does the height at particular places depend ? a. Where are the highest tides ? 
Why 1 b. Velocity of the tide wave ? c. Atmospheric tides ? 



CHAPTER XII. 

THE INFERIOR PLANETS. 
I. MERCURY. $ 

205. Mercury is remarkable for its small size, its swift 
motion, and the great inclination and eccentricity of its 
orbit. It is, as far as is positively known, the nearest planet 
to the sun. 

a. Name and Sign. — This planet probably derived its name from 
the swiftness of its motion, Mercury being, in the heathen mythology, 
the " messenger of the gods." The sign s is supposed to represent 
the caduceus, or wand, which the god is always seen, in the pictures 
of him, to carry in his hand. 

b, Vulcan. — Reference is made in Art. 16 to a planet supposed by 
some to exist between Mercury and the sun ; the following are the cir- 
cumstances connected with its supposed discovery : — On the 26th of 
March, 1859, a small dark body was seen to pass over a portion of the 
sun's disc, by M. Lescarbault, a French physician, but an amateur of as- 
tronomy ; and this appeared to him to indicate the existence of a planet 
whose orbit must be included within that of Mercury. From the 
observations which he made with his rude instruments, he calculated 
its period at about 20 days ; its distance, 14,000,000 miles ; and the 
inclination of its orbit, about 12°. On publishing this fact, the cele- 
brated French astronomer and mathematician, Leverrier, visited him, 
and after closely questioning him as to his means and method of 
observation, was completely satisfied of the truth of his statements. 
Singular to say, however, no other observer has been able to detect 
any indications of such a planet ; but, on the contrary, M. Liais, an 

Questions.— 205. For what is Mercury remarkable ? a. Its name and sign ? b. 
Supposed discovery of Vulcan? 



150 MERCUEY. 

astronomer of skill and experience, who happened to be engaged in 
observations of the sun, at Rio Janeiro, at the identical moment of M. 
Lescarbault's alleged discovery, asserted positively that no planetary 
object was visible at that time. The existence of any planet inferior 
to Mercury is therefore considered very doubtful. 

206. Mercury and Venus are known to be inferior planets, 

1. Because their greatest elongation is always less than 90° ; 

2. Because they exhibit all the different phases which are 
presented by the moon ; and, 3. Because they are seen, at 
the time of a transit, to pass across the sun's disc. 

a. A superior planet also exhibits phases, but it must always show 
more than half the disc ; that is, it must present the full or gibbous form. 
An inferior planet, however, in passing between the points of extreme 
elongation, presents the crescent form, and, in inferior conjunction, 
either totally disappears or is projected, in the form of a small round 
black spot, upon the disc of the sun. 

207. The greatest angular distance of an inferior planet 
from the sun, during any single revolution, is called its 
extreme elongation. The greatest extreme elongation of 
Mercury is 28|° ; the least, 18°. 

a. This large variation in the extreme elongation is an indication 
that Mercury revolves in an orbit of considerable ellipticity, since 
this angle depends upon the relative distances of Mercury and the 
earth from the sun. It must be greatest when the earth is in perihe- 
lion and Mercury in aphelion, and least when the earth is in aphelion 
and Mercury in perihelion ; while the mean distance of each would 
give the mean value of this element. 

In Fig 93 let S be the sun, E, the earth, and M, Mercury at the point of 
extreme elongation, ME being tangent to the orbit, andSME a right 
angle. It will be obvious that M E S, the angle of extreme elongation, 
will be at its maximum when S E is the shortest and S M the longest ; and 
at its minimum when these are reversed ; because its size depends upon 

Questions. — 206. How are Mercury and Venus known to be inferior planets? a. 
What phases do the inferior and superior planets present ? 20T. Extreme elongation ? 
What is it in the case of Mercury ? a. "Why so variable ? Give the calculation from 
the diagram. 



MERCURY 



151 




the ratio of S M to S E, being greatest when 
the ratio is greatest. The perihelion dis- 
tance of the earth is about 90,000,000 miles, 
the aphelion distance of Mercury is about 
42,600,000 miles. For these values the ratio 
of S M to S E would be about .473 ; and the 
angle corresponding to this is 28° IS'. The 
least ratio of these lines is .3, and hence, the 
least angle, 18° ; while the mean ratio is .387 
(nearly), indicating an angle of 22° 47', 
which is therefore the mean value of this 
element. 

208. The aphelion distance of Mercury from the sun is 
about 42,600,000 miles ; its perihelion distance, 28,100,000 
miles ; and its mean distance, therefore, nearly 35,400,000 
miles. 

a. The Distance Calculated. — The distance of an inferior planet 
can be determined by its extreme elongation ; for (Fig. 93) S M is 
equal to S E multiplied by the sine of the angle S E M. Now, if the 
angle is 28° 15', its sine (or ratio of S M to S E) will be .473, and hence, 
taking the perihelion distance of the earth, 90,000,000 X .473 = 
42,600,000, which is the aphelion distance of Mercury. 

b. The mean distance of any planet from the sun can be calculated 
by Kepler's third law, when we know the sidereal period. In the case 
of Mercury, this is very nearly 88 days ; and hence, as the squares of 
the 'periodic times are in proportion to the cubes of the mean distances, 
(365|) 2 :(88) 2 : : (91,500,000) 3 : the cube of the mean distance of Mercury, 
which, if the proportion be worked out and the cube root extracted, 
will give 35,400,000 (nearly) ; and this is the true value of this ele- 
ment. [If the pupil is sufficiently advanced, it will be well for the 
teacher to show how this calculation may be facilitated by employing 
a table of common logarithms.] 

c. The difference between the aphelion and perihelion distances of 
Mercury, it will be seen, is 14,500,000 ; hence its eccentricity is 7,250,- 
000 miles, which is nearly .205 of its mean distance, or about 12 times 
as great as that of the earth. 

Questions. — 20S. What are the aphelion, perihelion, and mean distances of Mercury ? 
a. How calculated ? b. How determined by Kepler's third law? c. Eccentricity — how 
found ? 



152 MERCUEY. 

209. The apparent diameter of Mercury, when greatest, 
is about 13 seconds, and when least, about 4^ seconds ; this 
difference being caused by the variations in its distance 
from the earth. 

a. When in inferior conjunction it is, of course, at the point nearest 
to the earth, and when in superior conjunction, at its farthest point 
from the earth. When Mercury is in superior conjunction and each 
planet is at its aphelion, they are the farthest possible from each other ; 
that is, 42,600,000 + 93,000,000 = 135,600,000 miles. When Mercury 
is in inferior conjunction and at its aphelion, while the earth is in 
its perihelion, they are nearest to each other ; that is, 90,000,000 — 
42,600,000 = 47,400,000 miles. 

210. The real diameter of Mercury is about 3,000 miles 
(more exactly, 2,962 miles). 

a. This is deduced from its distance and apparent diameter by the 
method explained in Art. 147, a. Suppose the apparent diameter is 
ascertained to be 12V, while its distance from the earth is 50,000,000 
miles. Then, the sine of 6y, which is .00002962, being multiplied by 
50,000,000 gives 1481, the semi-diameter. 

b. A clearer idea may be formed of the apparent diameter of a 
planet by comparing it with that of the moon, which subtends an 
angle of more than 1,800" ; consequently, Mercury, when it appears 
as a thin crescent near inferior conjunction, subtends an angle equal to 
only about -,-£o or Te o P ar * 0I " tne moon's disc ; while when it recedes 
to its greatest distance, it is about - 4 -^o part. 

c. The oblateness of the planet ha,p been generally considered very 
small ; but one astronomer (Dawes), in 1848, gave it at -fa, which would 

Fig. 94. be nearly ten times as great as that of the 

earth. 

d. Volume, Mass, and Density. — The 
volume of Mercury is about .052 of the 
earth's ; and the mass has been estimated 
at about .063 ; hence, its density must be 

COMPARATIVE VOLUMES OF MEB- ' J 

cuky and the earth. .063 h- .052 = 1.12, the earth 's being 1 ; 




Questions.— 209. What is the apparent diameter when greatest? When least? a. 
Why so variable ? 210. What is the real diameter? a. How found? b. How does it 
compare with that of the moon? e. Is Meroury oblate ? d. What is its volume? 
Mass? Density? 



MEECURY. 153 

and since this is 5.67 of water, 5.67 X 1.12 = 6.35, must be the density 
as compared with water. To find the mass of Mercury is so difficult 
a problem, that these figures can not altogether be relied on. There 
is but little doubt, however, that its density exceeds that of the 
earth by an eighth to a fifth. The famous French mathematician Le 
Verrier estimates it at more than twice that of the earth. 

e. Superficial Gravity at Mercury. — Since gravity varies directly 
as the quantity of matter, and inversely as the square of the distance 
from the centre, at the surface of Mercury it must be nearly (it o u) 2 X 
.063, or £/ X .063 = .448 (nearly). Hence, a body that weighs a pound 
at the surface of the earth would weigh less than half a pound at 
Mercury. If we should be transported to this planet, we should ap- 
pear to have more than twice as much muscular power, since the 
resistance to our efforts would be diminished more than one-half. 

211. Mercury is supposed to perform a diurnal rotation 
in about 24 hours (24 h 5 m 28*). 

a. This was discovered by the celebrated German astronomer, 
Schroeter, at the end of the last century, by examining daily the ap- 
pearance of the cusps, or extremities of the crescent form of the 
planet, which instead of being pointed are sometimes obtuse, owing to 
irregularities on the surface of the planet, and during one rotation 
undergo certain changes in form, which enabled the astronomer to dis- 
cover the period. He also thought that he had discovered certain dark 
bands across the disc, and was enabled to measure the height of some 
of the mountains, which, according to his computations, are very high, 
some of them more than ten miles, — an enormous altitude for so small a 
body. These discoveries have not, however, been confirmed by the 
observations of other astronomers. Sir John Hercchel, with all his 
advantages for telescopic observation, and his great experience and skill 
as an observer, states that " all that can be certainly affirmed of Mer- 
cury is, that it is globular in form and exhibits phases*; and that it is 
tco small and too much lost in the constant and close effulgence of the 
sun to allow the further discovery of its physical condition." 

b. Mercury is a very difficult object to see in consequence of its 
nearness to the sun ; for it is generally entirely involved in the twi- 
light or obscured by the mists that float near the horizon. Copernicus, 

Questions.— e. Hour does gravity, or weight, at Mercury compare with that at the 
earth? 211. In what time does Mercury rotate? a. How and hy whom was this dis- 
covered ? 6. Why is Mercury a difficult object to see ? 



154 MERCURY. 

it is said, regretted at his death that he had never been able to obtain 
a view of it. In lower latitudes, where the diurnal circles are more 
nearly vertical, the twilight shorter, and the atmosphere less clouded, 
it is more easily seen. The fact that it was so well known to the 
ancients as a planetary body proves to us that they were very careful 
and diligent observers. When viewed through a telescope, it looks 
intensely brilliant, on account of its proximity to the sun ; and this 
excessive brilliancy serves to prevent the clear observation of any spots 
on the disc which would afford positive indications of its axial rotation. 
It has, nevertheless, been very diligently observed by astronomers. 
Arago states that at the observatory of Paris alone, more than two hun- 
dred complete observations of it were made from 1836 to 1842. 

212. Mercury performs its sidereal revolution in about 88 
days (87 d 23 h 16 m ) ; its synodic period is about 116 days. 

a. The sidereal period may be ascertained by observing when the 
planet is at either node, and noticing the interval of time that elapses 
before it returns to the same node. The synodic period can be cal- 
culated on the principle already explained. Thus, 365£ days -s- 
87.968 days = 4.152, which is the number of sidereal revolutions in a 
year ; hence there must be 3.152 synodic revolutions, or one less than 
the sidereal ; and 365^ days -4- 3.152 = 116 days (nearly). 

Or the synodic period may be found by observation, and the sidereal 
period deduced from it on the same principle. (365^-^-116 = 3.152 .'. 
3651-^4.152 = 87.968.) 

213. The apparent diameter of the sun as seen at Mer- 
cury varies considerably, owing to the great difference in its 
distance at aphelion and perihelion. When in the former 
position it is nearly 69'; in the latter, 104'; being when 
least more than twice, and when greatest more than 3| 
times that of the sun as seen from the earth. 

a. Light and Heat at Mercury, — The light and heat received 
from the sun when Mercury is in perihelion must be greater than in 
aphelion, in the proportion of 2.27 to 1 ; that is, in the former, about 
2\ times as great as in the latter ; for the light and heat vary in 

Questions.— 212. What is the sidereal period of Mercury ? Its synodic period ? a. 
How may one be deduced from the other ? 213. Apparent diameter of the sun at Mer- 
cury ? a. Its light and heat ? 



MERCURY. 155 

proportion to the area of the sun's disc, and this is as the square of 
the apparent diameters ; or as (104) 2 to (69) 2 , or as 2.27 to 1. On the 
same principle, the average amount of light and heat received by 
Mercury, is to that received by the earth as the square of the mean 
apparent diameter of the sun at that planet (83') 2 is to that at the earth 
(32') 2 ; that is, as 6889 is to 1024 or as 6| (nearly) to 1. In other words, 
the light and heat at Mercury are nearly 6| times as great as at the 
earth. This, of course, may be very much modified by other circum- 
stances. 

b. Seasons at Mercury. — Since the light and heat are more than 2^ 
times as great in perihelion as in aphelion, there must be a succession 
of seasons on the planet depending entirely on the eccentricity of its 
orbit, summer occurring when the planet is in perihelion", and winter 
when it is in aphelion. If the axis of the planet is inclined to its 
orbit, another succession of seasons must occur, which, if they coincide 
with the former, must, in one hemisphere, augment the intensity of the 
heat, and in the other, increase that of the cold ; while, if they do not 
coincide, the one cause must tend to counteract the effects of the other, 
and thus diminish the great extremes of heat and cold. 

214. Transits of Mercury. — When the latitude of Mer- 
cury or Venus, at the time of inferior conjunction, is less 
than the semi-diameter of the sun, a transit must occur, 
the planet appearing on the sun's disc like a small, round, 
and intensely black spot, and moving across it from east to 
west. 

a. It appears to move across the disc from east to west for the same 
reason that the solar spots appear to move in that direction (Art. 152, b). 
The planet's velocity being faster than the earth's, the planet passes 
the earth actually from west to east, but in a direction opposite to the 
diurnal motion of that part of the earth on which the observer stands ; 
hence the apparent motion is westward, since east is in the direction 
of the rising sun, and this must be the point toward which anyplace 
on the earth turns. 

b. Transit Limits.— The limits in latitude within which a transit 
can occur correspond to the semi-diameter of the sun ; and as Mer- 



Qttestions.— &. Seasons at Mercury? 214. "When do transits occur ? a. Appearance 
of the transit ? Why does the planet appear to move from east to west ? 6. What 
are the transit limits ? 



156 vestus. 

cury's orbit is inclined to the ecliptic at an angle of 7°, it can easily be 
computed that the planet, at inferior conjunction, must be within 
about 2° of longitude from the node for a transit to occur. 

c Times of the Occurrence of Transits. — The longitudes of 
Mercury's nodes are 46° ( Q ) and 226° ( J? ) ; hence they are in Taurus 
and Scorpio, and the earth arrives at the line of nodes in May and 
November of each year. Transits must, consequently, occur in these 
months ; and this will continue to be the case for a long time, 
because the nodes change their position on the ecliptic only about 13' 
in a century. Because 7 sidereal periods of the earth are very nearly 
equal to 29 (29.064) of those of Mercury ; and 13 of the former are 
nearly equal to 54 (53.98) of the latter, transits must, as a general 
thing, occur at intervals of 7 or 13 years, at the same node. Owing, 
however, to the great inclination of the orbit, and the consequent 
small transit limit, these periods can not be relied on ; and it requires a 
period of 217 years to bring round the transits exactly in the same 
order. The last transit occurred on the 12th of November, 1861 ; the 
next will occur on the 5th of November, 1868. 

II. VENUS. $ - 

215. Ve:n"US is in appearance the most brilliant and beau- 
tiful of all the planets, and is remarkable for its close 
resemblance to the earth, both in size and mass. 

a. Name and Sign. — Venus, in the pagan mythology and religion, 
was the goddess of beauty, and hence the name was appropriately 
applied to the most beautiful of the planets. The sign is sup- 
posed to represent a mirror having a handle at the bottom. By the 
ancients, this planet, when an evening star, was called Hesperus or 
Vesper, the former being a Greek word, and the latter a Latin word, 
each meaning the evening. When a morning star, it was called 
Phosphorus or Lucifer, the former, in Greek, signifying that which 
brings the light ; and the latter meaning the same thing in Latin. 
These were at first supposed to be different bodies. 

216. The phases of Venus exactly resemble those of the 



Questions. — c. In what montfis do transits occur ? Why ? At what intervals do they 
occur? Why? 215. For what is Venus remarkable? a. Its name and sign? 216. 
What phases does it exhibit ? 



VENUS, 



157 



moon, and when viewed with a telescope are very interest- 
ing and beautiful, clearly proving that this planet revolves 
within the earth's orbit. 

217. When the planet is in superior conjunction its full 
disc is visible, which gradually diminishes until, at the 
time of greatest elongation, only half of the disc is seen ; 
after which the planet still continues to wane until, when 
near inferior conjunction, it assumes the form of a slender 
crescent. 

218. When the planet is full, its apparent diameter is least, 
since it is then farthest from the earth ; but near inferior 
conjunction, its apparent diameter is greater than at any 
other time, except when it is seen during a transit. 

The accompanying diagram (Fig. 95) shows the phases of Venus during 
one synodic period. The difference in size when the planet is full and 
when it has the crescent form, will be obvious. This difference, however, 

Fig. 95. 




PHASES OF VENUS. 

is greater than here presented ; the apparent diameter in inferior conjuction 
being more than six times as great as it is when in superior conjunction. 



Questions.— 21 T. When is it full, half, and crescent ? 218. When is its apparent 
diameter greatest ? When least ? 



158 VENUS. 

219. The extreme elongation of Venus never exceeds 
47f °, its average being about 46°. 

a. This small amount of variation indicates that the orbit has very 
little eccentricity. 

b. Venus is most brilliant when the elongation is about 40°, and 
when its apparent diameter is about 40", and about \ of the entire 
disc is visible, this portion giving more light than phases of greater 
extent, because the latter are presented at so much greater distances. 
During every eight years, when the planet has its greatest north lati- 
tude and is 40° from the sun, its brilliancy is so dazzling that it is 
visible in full daylight, and casts a sensible shadow in the evening. 
This was the case in Feb. 1862, and had been often observed previously. 

220. The aphelion distance of Venus from the sun is 
about 66,600,000 ; the perihelion distance, 65,700,000 ; its 
mean distance being about 66,150,000. 

a. The mean distance can be calculated by Kepler's third law ; and 
the aphelion and perihelion distances by the greatest and least extreme 
elongations, as in Art. 208. 

flgp [The pupil should be required to make the calculations in each 
case. The ratios or sines of the angles can be found by consulting any 
ordinary table of natural sines. The term natural is employed to distin- 
guish these ratios from the logarithmic expression of them.] 

b, The absolute eccentricity of Venus, it will be seen, is only about 
450,000 miles, or less than .0069 of its mean distance. So nearly does 
the orbit resemble a circle. 

221. The apparent diameter of Venus, when greatest, is 
66±" ; and when least, somewhat less than 10". At its 
mean distance (91 millions of miles) from the earth it is 
about 17" ; and therefore its real diameter is 7510 miles. 
(Art. 210.) The compression or oblateness of the planet 
is exceedingly small. 

a. Volume, Mass, and Density. — The volume of Venus is about 
.85 of the earth's ; while its mass is .89 ; hence its density must be 



Questions. — 219. Extreme elongation ? a. Why but slightly variable ? b. When is 
Venus most brilliant ? 220. Distances of Venus ? a. How calculated ? b. Eccentric- 
ity ? 221. Apparent and real diameter ? a. Volume, mass, and density ? 



venus. 159 

.89-^.85 = 1.047 (nearly), or very little greater than that of the 
earth. 

b. Superficial Gravity.— This is found as in Art. 210, e, (f Hff X 
.89 = .98 ; that is, a pound at the earth's surface would weigh only .02 
less at the surface of Venus. 

222. The diurnal rotation of Venus is performed in 23 h 
21 m 19 3 . 

a. This is the period as determined by Schroeter in 1789, by discov- 
ering a luminous point in the dark hemisphere a little beyond the 
southern horn of the planet, indicating the existence there of a high 
mountain. By watching its periodic changes, he was enabled to 
deduce the time of the rotation ; which agreed very nearly with the 
result attained in 1667, by Cassini, and was subsequently confirmed 
by the observations of other astronomers. 

6. Mountains in Venus. — According to Schroeter, there exist mount- 
ains of immense height on the surface of Venus ; the elevation of the 
loftiest being equal to xio of the planet's radius, which would be 
about 27 miles, or five times the altitude of the loftiest terrestrial peak. 

Fig. 96. 




TELESCOPIC VIEWS OP VENT/S. 

While other astronomers have detected the existence of mountains on 
the planet, their observations do not confirm the statements of 
Schroeter as to their height. Very great irregularities on its sur- 
face are, however, indicated by the jagged character of the termi- 
nator, by the shading of its edge, and by the blunt or broken 
extremities of its cusps. The shading is supposed to be caused by the 
long shadows cast by the mountains as the sun shines obliquely upon 
them. [See Fig. 96.] The telescopic observation of Venus is attended 

Questions. — b. Superficial gravity ? 222. Time of diurnal rotation ? a. How deter- 
mined ? 6. Mountains in Venus ? What indications in the telescopic views ? 



160 VENUS. 

with great difficulty on account of the intense brilliancy of its light, 
which dazzles the eye and augments all the imperfections of the 
instrument. 

223. There are undoubted indications that Venus is sur- 
rounded by an atmosphere of considerable height and 
density. 

a. This is shown by several circumstances : 1. When the planet 
was seen as a narrow crescent, Schroeter remarked a faint light pro- 
jecting beyond the proper termination of one of the horns into the 
dark part of the planet. This has been seen by other observers, and is 
supposed to be due to the existence of an atmosphere refracting the 
light of the sun. 2. By observing the concave edge of the crescent, it 
is found that the enlightened part does not terminate suddenly, but that 
there is a gradual fading away of the light into the dark portion of the 
planet's surface, this being obviously occasioned by a reflection of the 
sun's rays, producing the phenomenon of twilight. 3. During the tran- 
sits of 1761 and 1769, the planet was observed, by several astronomers, 
to be surrounded by a faint ring of light, caused, as it has been sup- 
posed, by the sun's rays passing through the planet's atmosphere. 
4. Clouds have been observed floating over the disc of the planet, and 
screening by their greater brilliancy its darker surface, which is occa- 
sionally seen between them. Such being the case, there must be water 
as well as air on the surface of Venus. 

224. The inclination of the axis of Venus has not been 
positively ascertained ; but it is supposed to be very great, 
according to several astronomers;, about 75°. 

a. This can be positively discovered only by observing spots on the 
disc, and noticing the direction of their apparent motion. This, in the 
case of Venus, is exceedingly difficult, owing to the intense brilliancy 
of its light and the density of its atmosphere. Cassini, as early as 
1666-7, saw one bright and several dusky spots, and others have been 
observed since that time by different astronomers, among whom, 
De Vico, at Rome, in 1839-41, appears to have attained the most reli- 
able results. 

Questions.— 223. Has Venus any atmosphere? a. What indications of it? 224. 
Inclination of the axis of Venus ? a. How discovered ? 



VENUS. 161 

225. If the axis of Venus has an inclination of 75°, its 
tropics must be 75° from its equator, and its polar circles 
75° from the poles. Hence it can haye only a torrid zone, 
which must be 150° wide, and frigid zones extending 75° 
from the poles. 

226. Seasons of Venus. — As the sun must arrive at the 
equator and depart to its greatest distance from it twice dur- 
ing each sidereal period, there must be two summers and 
two winters at this part of the planet, and a summer and 
winter at each of the poles, which must suffer a transition 
from the burning heat of a vertical sun and constant day, 
to the intense cold of perpetual night, each lasting more 
than 112 days. 

Mg. 97. 




Fig. 97 exibits the relative positions of the tropics and polar circles, the 
former being the nearest to the poles. The sun is represented as in the 
northern solstice ; and it will be seen that all places situated more than 15° 
north of the equator have constant day, and those more than 15° south of 
it, constant night. Hence there must be winter at the equator and within 
the south polar circle, and summer within the north polar circle. In 
one-fourth of the year, when the sun will have arrived at the equator, 
there will be equal day and night all over the planet, summer at the equa- 
tor, autumn within the north polar circle, and spring within the south polar 
circle. 

Fig. 98 exhibits the planet at each of the equinoxes and solstices : To an 
inhabitant of the northern hemisphere of Venus, at A the sun is in the vernal 
equinox; B, the summer solstice; C, the autumnal equinox; and D, the 

Questions. — 225. Zones of Venus ? 226. Seasons ? Ulustrate by the diagram. 



162 VENUS. 

winter solstice. To an inhabitant of the southern hemisphere, these 
would, of course, be reversed. 

Fig. 98. 




SEASONS OP VENT/S. 

227. Venus performs its sidereal revolution in about 224§ 
days (224 d 16 h 49 m ) ; its synodic period is about 584± days. 

a. For its sidereal period is 224.7 days, and 365.25 -f- 224.7 = If ; 
hence If — 1 = f , is the part of a synodic revolution performed in 
365i days ; and 365^ -h f = 584^ days. [See Art. 212, a.] 

b. Division of the Synodic Period. — Since the mean value of 
the extreme elongation of Venus is 46°, which is the angle M E S 
(Fig. 93), the angle at the sun M S E must be 90° — 46° = 44°. There- 
fore the planet, in passing from M to the other point of extreme 
elongation, has to gain on the earth 88° ; and the time required 
for this must bear the same ratio to 584£ days as this angle bears to 
360°. Consequently, the synodic period is divided into the following 
intervals : f£<j X 584^ days = 142.9 days, the interval between the time 
of greatest elongation before and after inferior conjunction, and f£§ 
X 584^- days = 441.1 days, the interval between the elongation before 
and after superior conjunction. One-half of each of these intervals 
will give the time from the greatest elongation to inferior conjunction, 
and that from greatest elongation to superior conjunction, respectively. 

Questions. — 227. Sidereal period? Synodic period? a. How calculated ? b. In- 
terval of time between the elongations and conjunctions? 



VEtfUS. 163 

c. Morning and Evening Star. — Since Venus must remain on 
each, side of the sun during 292 days, or one-half the synodic period, 
it must be a morning and evening star alternately for that time 

228. The distance of Venus from the sun being a little 
more than ^ the distance of the earth, the apparent diame- 
ter of the sun must be If as great, or about 45 '. Hence the 
solar light and heat must be more than twice as great. 

a. For these vary inversely as the squares of the distances ; and as 
the ratio of the distances is .723, (.723) 2 , or about .52 will be the ratio 
of the light and heat of the earth to those of Venus. This, of course, 
may be very much modified by the influence of its atmosphere. 

229. Teaksits of Venus. — The orbit of Venus is in- 
clined to the ecliptic at an angle of 3 \° (3° 23' 29") ; and 
therefore a transit can take place only when the planet is at 
or near one of its nodes. The transits of Venus are of 
great interest and importance, because they afford a means 
of determining the parallax of the sun, and consequently its 
distance from the earth. 

a. History of Transit Observations. — These transits are of rare 
occurrence. Kepler, in 1629, predicted that a transit would occur in 
1631, and that no other would occur until 1761. His prediction, how- 
ever, was not confirmed by observation, for the transit of 1631 
occurred during the night ; and in 1639 the first observation of a 
transit was made by a young English astronomer, named Horrox. No 
other occurred till 1761 and 1769 ; and these were observed with great 
care in different parts of the world, in order to apply the method of 
finding the solar parallax, first suggested by Gregory, a celebrated 
mathematician, in 1663. King George III., in 1769, despatched, at his 
own expense, an expedition to Otaheite, under the command of the 
celebrated navigator, Captain Cook, in order that observations of the 
transit might be taken in this distant spot. Other nations sent in dif- 
ferent directions similar expeditions. The average result of these 
different observations assigned as the true solar parallax 8.5776", which 

Questions. — c. How long does Venus remain a morning or evening star? 228. 
Solar light and heat at Venus? a. Why? 229. When do transits occur? Why im- 
portant ? a. History of transit observations ? 



164 VENUS„ 

has, within a very few years, been found to be somewhat too small. 
The next transit will occur in 1874. 

b. Times of the Occurrence of Transits. — The longitudes of the 
nodes of Venus are about 75° (£\), and 255° (\J) : hence, they are> in 
the 15th degree of Gemini and Sagittarius ; and as, therefore, the earth 
arrives at the line of nodes early in June and December, the transits 
must occur in these months i and will continue to do so for a long time, 
since the longitude of the nodes diminishes, according to Le Verrier, at 
the rate of less than 18' in a century. 

c. Because 8 sidereal periods of the earth are very nearly equal to 
13 of Venus, transits often occur at intervals of eight years ; when, 
however, two transits have occurred at this interval, another can not 
be expected before 105^ years. Thus, the next transit will happen in 
December, 1874 ; and another in 1874 + 8 = 1882 (December 6th). The 
next will not occur till June 7th, 2004, 121 | years afterwards. The 
transits are thus repeated at intervals of 8, 105^, 8, 121i, 8 years, etc. ; 
acccording as they occur at one or the other node. 

d . How to Find the Sun's Parallax by the Transits of Venus. — 
By the greatest elongation, the distance of an inferior planet from the 
sun can be found, provided we know the earth's distance. We, in fact, 
only find by this method the ratio of one distance to the other ; and 
this is known, therefore, independently of the solar parallax. 

Fig. 99. 



TBAN8IT OF VENTTS. 



In Fig. 99, let A and B be the positions of two observers stationed at op- 
posite parts of the earth, and V, the place of Venus at the time of a transit. 
The observer at A will see the planet projected on the sun at a, and the 
observer at B, at b ; and if each observer notice exactly the time required 



Questions.— b. Which are the node months ? Why ? c. Epochs of the occurrence 
of transits ? d. How is the solar parallax found by transit observations? 



VENUS. 165 

by the planet to cross the disc, he can, since its hourly motion is known, 
easily calculate the length of the chord which it appears to describe at each 
place ; and a comparison of the length of these chords will give the dis- 
tance between a and b in seconds of space. Now, if Venus were exactly 
half-way between the earth and sun the distance a 6 as seen from the earth 
would be exactly the same as A B seen from the sun ; and therefore would be 
twice the parallax. But the distance of Venus from the sun is known to 
be .723 of the earth's distance; and consequently AV, its distance from 
the earth, must be 1— .723 = .277 ; so that the ratio of a V to A V is Iff = 2.6 
(nearly). But a b bears the same ratio to A B as a V does to A V : hence, 
the distance a b must be 2.6 x 2 or 5.2 times the solar parallax. Suppose, 
therefore, this distance should be found by observation and calculation to 
be 46!" ; then 46§" ■*- 5.2 = 8.94" would be the true parallax. The advan- 
tage afforded by this method is, that because the distance of Venus from the 
earth is so much less than from the sun, a b is enlarged in the same pro- 
portion, and thus rendered more susceptible of exact measurement. Thus, 
it will be obvious that whatever error arises in determining a &, affects the 
parallax less than one-fifth. Practically, it is impossible that the observers 
should be as far apart as A B ; but whatever their distance from each other, 
it can be easily reduced to the conditions represented in the diagram. 

APPARENT MOTIONS OF THE INFERIOR PLANETS. 

230. The apparent motions of Mercury and Venus are 
sometimes from west to east, and sometimes from east to 
west. The former are said to be direct ; the latter, retro- 
grade. At certain intermediate points, the planet appears 
to remain for a short time in the same point of the heavens, 
and is then said to be stationary. 

a. The student must clearly understand that these motions and 
stationary points have reference to the stars, not to the sun ; the appa- 
rent place of the latter is constantly changing on account of the 
motion of the earth. These phenomena are illustrated in the annexed 
diagram, 

Let S (Fig. 100), be the place of the sun, the inner circle the orbit of an 
inferior planet ; the outer circle that of the earth. Let also a, b, c, d, etc., 
be the positions of the planet at unequal intervals of time between the points 

Questions. — 230. What apparent motions have Mercury and Venus ? When are 
they said to be stationary ? a. Does this refer to the sun or the 6tars? Explain the 
phenomena from the diagram. 



166 



VENUS. 



of extreme elongation, a and g ; and A, B, C, D, etc., the places of the 
earth at the same time ; while 1, 2, 3, 4, etc. , represent the apparent places 
of the planet, as seen in the sphere of the heavens. In passing from g, 
the western point of extreme elongation, through o, the place of superior 

Fig. 100. 




APPARENT MOTIONS OP VENUS AND MERCURY. 

conjunction, to a, the eastern point of extreme elongation, the planet evi- 
dently must appear to move toward the east ; and when it arrives at a, the 
earth being at A, it still continues to he direct for a short time ; for while 
going from a to 6 its motion is so oblique that the earth passes it, so that 
when the latter arrives at B, the planet appears to have moved from 1 to 2. 
Its elongation is not, however, increased since the sun itself has moved far- 
ther to the east. While the planet is going from b to c, and the earth from 
B to C, the former does not appear to change its position at all ; for the 
lines B b 2 and C c 3 are parallel, and consequently indicate no change of place 
among the stars, and 2 is to be considered, therefore, as identical with 3. 
The reason of the planet's appearing stationary, it will be seen, is that the 
obliquity of its motion exactly counterbalances the difference between its 
actual velocity and that of the earth ; b is, therefore, to be considered the 
stationary point. At d, the planet is in inferior conjunction, having overtaken 
the earth, and is seen at 4, to the west of its previous position. In passing 



vekus. 167 

from d to g the same phenomena are presented in the reverse order ; at e it 
becomes stationary, remaining so till it reaches /, where it ceases to he ret- 
rograde, appearing to move while going from /to g, from 6 to 7. In going 
from c to e, the two stationary points, it has evidently changed its direction 
among the stars, not by the actual distance 3, 5, but by the angle contained by 
the lines 3 c C and 5 e E when produced until they meet in some point be- 
low C D E. This angle, or the arc by which it is subtended, it is obvious, is 
quite small ; it is called the arc of retrogradation. From the above ex- 
planation the following statements will be understood. 

231. An inferior planet appears stationary at two points 
of its synodic revolution, between the extreme elongations 
and inferior conjunction. Its motion is retrograde in 
passing through inferior conjunction from one stationary 
point to the other ; and direct in passing through superior 
conjunction, between the same two points. 

a. The stationary points of Mercury vary from 15° to 20° of elonga- 
tion from the sun ; those of Venus generally occur when its elongation 
is about 29°. (See Fig. 95). 

b. The time during which Mercury retrogrades is about 22 days; 
Venus, 42 days. The mean arc of retrogradation of the former is about 
12£° ; of the latter, 16°. The stations of both are, of course, but of 
very short duration. 

Qttestions.— 231. When does at) inferior planet appear stationary? When is its 
motion direct ? When, retrograde ? a. Where are the stations of Mercury and Venus ? 
b. During how many days does each retrograde ? How long are the arcs of retrogra- 
dation? 



CHAPTER XIII. 

THE SUPEKI0R PLANETS. 
I. MARS. $ 

232. Mars, the fourth planet from the sun (the most 
distant of the terrestrial planets), is remarkable for its small 
size and the red color with which it shines among the stars. 

a. Name and Sign. — This redness of its appearance makes it easily 
distinguished among the other heavenly bodies, and doubtless gave 
rise to its name ; Mars, in the heathen mythology, being the god of 
war. Its sign is a shield and spear. 

233. Phases. — When Mars is in opposition or conjunc- 
tion, its disc is full ; when between these points, it is gibbous. 
More than half of its disc is, therefore, always visible. 

a. The reason of this will be apparent after a little consideration. 
In opposition and conjunction, the hemisphere presented to the earth 
exactly coincides with the illuminated disc ; hence, the planet appears 
full. The amount of diminution of the full disc is obviously equal to 
the angle formed at the centre of the planet by lines drawn to the 
earth and sun. (See Fig. 75.) As, in the case of a superior planet, this 
angle is always less than a right angle, the amount of dimunition 
must be less than one-half of the disc ; for a right angle would include 
one-quarter of the whole surface, which is, of course, one-half of the 
disc. Therefore, the planet can present no other than the full or 
gibbous phase. 

234. The Apparent Motions of a superior planet, like 

Questions.— 232. For what is Mars remarkable? a. Name and sign? 233. What 
phases does it exhibit ? a. How is this explained ? 234. What apparent motions have 
the superior planets ? 



MAES. 169 

those of an inferior planet, are either direct or retrograde ; 
and as its motion changes from one to the other, it appears 
for a short time to be stationary. 

235. The motion appears to be retrograde for a short dis- 
tance before and after opposition, and direct in the other 
part of its orbit. The retrogradation of the planet is 
caused by the greater velocity of the earth ; so that as the 
latter body moves toward the east, it passes the other, and 
thus makes it appear to move toward the west. When the 
motion of the earth is sufficiently oblique to counteract the 
excess of its velocity, the two bodies move on together, and 
the planet appears to be stationary. 

a. The arc of retrogradation in the case of the superior planets 
is very small. The following is the mean value of each : Mars, 15° ; 
Jupiter, 10° ; Saturn, 6|° ; Uranus, 3f ° ; Neptune, about 2°. 

b. Mars retrogrades from 60 to 80 days, according as it is in perihe- 
lion or aphelion; Jupiter continues to retrograde during about 4 
months ; Saturn, about 4£ months ; Uranus, about 5 months ; Neptune, 
about 6 months. 

c. Mars becomes stationary when its elongation is about 140° ; 
Jupiter, 115° ; Saturn, 110° ; Uranus, 103° ; Neptune, 97£ . 

236. The aphelion distance of Mars is about 152,300,000 
miles ; its perihelion distance, 126,300,000 ; hence, its mean 
distance is about 139,300,000. 

a. Since the periodic time of Mars is 1/ 322 d , we have, by Kepler's 
third law, (365^) 2 :(687|) 2 : : (91,500,000) 3 : the cube of the distance of 
Mars, which, by working out the proportion, will give very nearly the 
mean distance above stated. 

ft. The distance can also be found approximately by observing the 
phase of Mars when it varies most from the full. The following is the 
method : — 

Let S (Fig. 101), represent the sun, E, the earth, and M, Mars, much 

Questions. — 235. When is the motion retrograde ? Why ? When is the planet sta- 
tionary ? Why ? a. What is the arc of retrogradation of each superior planet ? 6. 
How long does each retrograde ? c. Where are the stationary points? 236. Distance 
of Mars from the sun ? a. How found by Kepler's third law ? b. How by the phase ? 



170 



MAES, 




Fig. 101 enlarged for convenience of illustra- 

tion. The earth is obviously at the 
point of greatest elongation as seen 
from Mars; and hence the angle 
S M E is the largest possible. But this 
is equal to a M d which measures the 
deviation of the disc from the full; 
for the arc b a = ed; and taking e a 
from each, there remain be = ad. Sup- 
pose this angle is measured and found 
to be 41° 4'. Then the sine of this angle 
being about .657, this must be the 
ratio of the distance of the earth to 
that of Mars ; and 91,500,000 -*- .657 = 
139,300,000 (nearly). This method is 
applicable only to Mars; since the 
other planets are so far distant that the angle of elongation corresponding 
to S M E, is very small ; and their deviation from the circular outline not 
large enough to be susceptible of exact measurement. 

c, A more general method, based upon the daily arc of retrograda- 
tion of the superior planets, is interesting as having been employed 
by the old astronomers, and more particularly by Kepler in those, 
investigations which resulted in the discovery of his third law. The 
following is a brief statement of this method : — 

Let S (Fig. 102), represent the sun, E e the daily arc of movement of the 
earth, and M m, that of Mars in opposition. In going from M to m, the 
planet obviously changes its direction backward among the stars by the 
angle d e o = e o E. Now, in the triangle o e S, the angle o is given, also the 

Pig. 102. 




angle E S e, since it is the amount of angular movement of the earth 
for the time ; hence, the third angle oeS becomes known ; and the ratio of 
o S to e S, since this is equal to the ratio of the sines of o e S and e 08. In 
the triangle o m S we have, in the same manner, the angles o and mSM, 
the latter being the angular movement of the planet, so that the ratio of 



Question. — c. How may the distance be found by the arc of retrogradation ? 



MARS. 171 

oStomS becomes known ; whence, combining tbe two results, we obtain 
the ratio of m S to e S, or that of the two distances ; on the supposition, 
however, that the orbits are circular ; but when the process is repeated in 
every variety of situation at which the opposition may occur, the average 
of the results will give a tolerably accurate determination. 

237. The eccentricity of the orbit of Mars is about 13 
millions of miles, or .093 of its mean distance. It is, there- 
fore, nearly 5^ times as great as that of the earth. 

a. Parallax of Mars and of the Sun. — Owing to the great eccen- 
tricity of the orbit of Mars, it sometimes, when in opposition, approaches 
very near to the earth ; for if it is in perihelion while the earth is in 
aphelion, the distance is 126,300,000—93,000,000 = 33,300,000. Ad- 
vantage was taken of this in 1862 to determine its parallax. It was 
arranged that several observers should station themselves at places in 
different hemispheres and record the zenith distance of the planet 
when on the meridian, as well as its distance from certain stars, so as 
to ascertain the amount of displacement in its position occasioned by 
the separation of the observers. These observations were made at 
Greenwich, Pulkova, Washington, Cape of Good Hope, Williamstown 
in Australia, and Santiago. 

An effort was also made to determine the parallax at a single obser- 
vatory, by observing the displacement in the apparent position of the 
body, occasioned by the rotation of the earth. For as the observer is 
not situated at the centre of motion, the planet can only appear pre- 
cisely in its true place, as to right ascension, when it is on the meridian ; 
and frequent observations made before and after culmination must 
show an average displacement, from which its parallax may be calcu- 
lated, and consequently its distance from the earth. From this may 
be deduced the earth's distance from the sun, and of course the solar 
parallax. The results of the different observations very nearly agreed, 
all showing the parallax as determined in 1769 to be too small. The 
average result is that now generally accepted (8.94"). Le Verrierhad 
previously assigned very nearly the same amount by calculations based 
upon the disturbances of the planets, which showed that the parallax 
needed correction in order to bring the observed perturbations into 
harmony with those theoretically computed. 

Questions. — 237. What is the eccentricity of the orbit of Mars? a. How to find the 
parallax of Mars, and the solar parallax ? 



172 MAES. 

238. The inclination of the orbit of Mars to the plane 
of the ecliptic is only about two degrees (1° 51'). 

239. Its sidekeal period is nearly 687 days ; its synodic 
period, 780 days. 

a. For 687 d — 365^=321^; hence, 687 d -s- 321|< i = 2.135, is the 
number of revolutions of the earth during the synodic period ; and 
365i d X 2.135 = 780 d (nearly). In Art. 64, the same method is applied 
fractionally ; thus, 365^ d = .532 of 687 d ; hence, the earth gains in one 
revolution 1 — .532 = .468 of a revolution upon the planet ; but she 
has to gain an entire revolution ; and 1 -r- .468 = 2.135 revolutions 
(nearly). 

240. The apparent diameter of Mars varies between 4" in 
conjunction and 30" in opposition. Its real diameter is 
about 4,300 miles. Its oblateness is about 5 J of its diame- 
ter, or 86 miles, and is consequently very nearly six times as 
great as the earth's. 

241. It performs its daily rotation in about 24J hours 
(24 h 37 m 42 s ), upon an axis inclined toward its orbit 28° 42' ; 
hence its obliquity is nearly the same as the earth's, and its 
variety of seasons also the same, except that they are nearly 
twice as long. 

a. Seasons of Mars. — The year of Mars contains 668 J 16 h of its 
own time, since its days are longer than those of the earth. Owing 
to the great eccentricity of its orbit, summer in the northern hemi- 
sphere is only about £ as long as in the southern ; but in consequence 
of its greater proximity to the sun, the light and heat are much 
greater (in the ratio of 145 to 100). Thus there is a complete compen- 
sation in the seasons of both hemispheres. Constant day at the north 
pole of Mars lasts during 297 of its days ; at the south pole, during 
372 days. Hence, constant night at the north pole is 75 days longer 
than at the south pole. 

242. The telescopic appearances of Mars are very 

Questions. — 238. Inclination of its orbit? 239. The sidereal and synodic periods? 
a. How deduced? 240. Apparent diameter? Real diameter? Oblateness? 241. 
Period of rotation ? a. Seasons ? 242. Telescopic appearances of Mars ? 



MAES. 



173 



interesting, exhibiting what seem to be the outlines of 
continents and seas, the former appearing of a ruddy or 
orange color, and the latter of a dusky greenish or bluish 
tint. 

243. Brilliant white spots are also seen alternately at the 
poles, produced, as it is conjectured, by accumulations of 
ice and snow during the long winters, particularly as they 
are seen to disappear as summer advances upon the poles. 

244. Evidences are also presented of an atmosphere, prob- 
ably of a density about equal to that of the earth. 

Fig. 103. 




NORTHERN AND SOUTHERN HEMISPHERES OF MARS.— M'ddler. 

a. With the exception of the moon, no body has been submitted to 
such a careful telescopic scrutiny as Mars. The utmost assiduity has 
been exercised particularly by Messrs. Beer and Madler in these 
researches, which were commenced by them in 1830, and continued 
at every opportunity for twelve years. A large collection of draw- 
ings of the various hemispheres presented by the planet was made 
by them, showing the positions and outlines of the spots seen on 
the disc, and clearly establishing their connection with the planet's 

Questions. —243. The white spots ? 244. Atmosphere? a. Observations of Mars ? 



174 JUPITEK. 

surface, and their general permanency. Considerable variety is, how- 
ever, exhibited in the forms of these spots, owing to the great diversity 
in the hemispheres presented. 

The annexed cut does not represent any actual telescopic views of the 
planet, since we are never so situated as to be able to see the whole of either 
the northern or southern hemisphere at any one time. It exhibits a combi- 
nation of a large number of telescopic appearances, the various dusky spots 
being placed together so as to show the forms of the different bodies of water 
and their relation to the continents ; the latter being indicated by the white 
spaces. These, through the telescope, appear of a ruddy color, and give 
this general tint to the planet. On the earth, the continents are islands, 
being encompassed by the water ; on Mars, it will be perceived, the bodies 
of water are lakes or seas, being entirely encompassed by the land. 

6. No entirely satisfactory cause has been assigned for the ruddy 
color of this planet. It is thought by Sir John Herschel to be due to 
" an ochrey tinge in the general soil, like what the red sandstone dis- 
tricts on the earth may possibly offer to the inhabitants of Mars, 
only more decided." Viewed through a telescope, the redness of its 
hue is very considerably diminished. 



II. JUPITER. 71 

245. Jupiter, the first of the major planets, is remakable 
for its great size, it being the largest of all the planets. 
It is also distinguished for the peculiar splendor with which 
it shines among the stars. 

a. Name and Sign. — This planet doubtless received its name on 
account of its superior magnitude and splendor, Jupiter, or Jove, in the 
ancient mythology, being the king of the gods. Its sign is supposed 
to be an altered Z, the first letter of Zeus, the name of Jupiter among 
the Greeks. 

246. The aphelion distance of Jupiter is 498,500,000 
miles ; its perihelion distance 453,000,000 miles ; hence its 
mean distance is 475,750,000. 

247. The eccentricity of its orbit is therefore 22*,750,- 

Qjtestions. — 6. Cause of its red color? 215. TTow is Jupiter distinguished? a. 
Name and sign ? 246. Distance from the sun ? 247. Eccentricity ? 



JUPITEE. 175 

000 miles, or about .048 of its mean distance; being 
relatively nearly three times that of the earth. 

248. The inclination of its orbit is very small, being only 
about 1° 19'. 

249. Its synodic period is found by observation to be 
about 399 days ; hence its sidereal period is about 4332 
days, or lly 315 d . 

a. For 399 d -f-365| d = 1.0921 revolution performed by the earth 
during the synodic period ; hence, Jupiter performs only .0921 of a 
revolution in 399 d ; and 399 d ^- .0921 = 4332 d +. 

250. The apparent diameter of Jupiter in opposition, 
when greatest, is about 50" ; in conjunction, 31" ; and at 
its mean distance is about 37". Its real equatorial diame- 
ter is about 87,500 miles. 

a. For the least distance of Jupiter from the earth is 453,000,000 — 
93,000,000 = 360,000,000 mile ; and the maximum apparent semi-diam- 
eter is 25", the sine of which is .0001215, and 360,000,000 X .0001215 
= 43,750 miles, which is the greatest, or equatorial, semi-diameter. 
Hence the diameter is 87,500 miles. 

251. The oblateness of Jupiter is very great, being 
about T \ of its mean diameter, or about 5,000 miles. 

a. Its polar diameter is therefore about 82,500 miles, and its mean 
diameter 85,000 miles. This remarkable degree of ellipticity in its 
figure is caused by the rapid rotation on its axis, which is performed 
in a little less than 10 hours (9 h 55^ m ) ; so that a point on the equator 
of this planet moves with a diurnal velocity of nearly 28,000 miles an 
hour, or 27 times as fast as at the earth. 

b. It has already been explained (129 a) that the oblateness of a 
planet's figure results from the action of the centrifugal force ; and it 
will be obvious that the degree of oblateness must depend on the 
velocity of rotation and the density of the body. It, in fact, varies 
directly as the square of the former, and inversely as the density, or 

Questions — 248. Inclination of its orbit ? 249. Its synodic and sidereal periods ? 
250. Apparent and real diameters? a. How found? 251. Oblateness? a. Equatorial 
and polar diameters ? Period of rotation ? Velocity? 6. How to find the oblateBess 
from the velocity ? 



176 



JUPITEE. 



the attraction of the body on its own matter. Thus, the velocity of 
Jupiter is about 2| times as great as the earth's [24 h -=- 10 h = 2|], but 
its density is only £ as great, and (2 1) 2 X 4 = 23 +. Therefore, if its 
density were as uniform as that of the earth, its oblateness would 
be, ^ X 23 = -j 1 ;,- of its diameter. The internal parts of Jupiter must 
therefore be very much more dense than the external, the latter prob- 
ably being considerably lighter than water. 

Fi S- 104 - c. Volume, Mass, and 

Superficial Gravity. — 

The volume of Jupiter is 
about 1244 times as great 
as the earth's ; for 85,000 
-^-7912 = 10.75, and 
SmS^M ' (10.75) 3 = 1244 (nearly). 

^P B^^^^^^^^H^ii "iBl * ts mass being only 301, 

its density is 301 -f- 
1244 = .242, or nearly \. 
The force of gravity at 
the surface of the planet 
must therefore be 301 -s- 
(10.75)* = 2.6+. So that 

COMPARATIVE MAGNITUDES OP THE EARTH AND JUPITER. a Qody Weighing 1 lb at 

the earth's surface would weigh 2.6 lbs at Jupiter's; and since a 
body falls through 16 feet in the first second of time at the earth's 
surface, it would fall more than 41 feet at that of Jupiter. 

d. Orbital Velocity. — This body, so inconceivably vast, is flying in 
its orbit with the velocity of 28,700 miles an hour, or nearly 500 miles 
a minute — a speed sixty times a great as that of a cannon ball. How 
tremendous is the exhibition of force here displayed ! 

252. The inclination of Jupiter's axis to that of its orbit 
is only 3° (3° 6'), much too small to cause any considerable 
change of seasons. 

a. The phenomena of constant day and night take place, therefore, 
only within two small circles extending 3° from the poles. Exactly at 
the poles, the d?y and night are alternately about six years long. The 
cold at these parts of Jupiter must be intense beyond any that we can 




Questions. — c. Volume, mass, and superficial gravity? d. Orbital velocity ? 252. 
Inclination of its axis ? a. What results from this? 



JUPITEE. 177 

conceive. The long absence of the sun, and its never rising more 
than 3° above the horizon, joined with the immense distance of the 
planet from that luminary, must all combine to intensify this rigor. 

b. Solar Light and Heat. — The light and heat of the sun at Jupi- 
ter must be less than at the earth, in the inverse ratio of (47o,50O,000) 2 
to (90,000,000) 2 , or of 27 to 1. This feeble supply of light and heat 
may, however, be compensated by a greater density of the atmosphere, 
a higher calorific or luminous capacity of the soil, or a greater amount 
of internal heat than that possessed by the earth. 

253. Belts of Jupiter. — When examined with a tele- 
scope the disc of Jupiter appears crossed by dusky streaks 
or belts, parallel to its equator, their general direction always 
remaining the same, although they constantly vary in num- 
ber, breadth, and situation on the disc. Sometimes the disc is 
almost covered with them ; while at others scarcely any are 
visible. 

254. These dusky bands or belts are supposed to be the 
body of the planet seen between the clouds that constantly 
float in its atmosphere, and are thrown into zones or belts by 
the great velocity of its rotation. The cloudy zones are 
more luminous than the surface of the planet, on account of 
their more powerful reflection of the solar light. 

a. The belts are not equally conspicuous, there being two generally 
which are more distinctly observable than others, and more permanent. 
These are situated, one on each side of the equator, and are sepa- 
rated by a clear space somewhat more luminous than the other parts 
of the disc. Toward the poles they are narrower and less dark ; and 
they imperceptibly fade away a short distance from the eastern and 
western edges of the disc, — a phenomenon due, evidently, to the thick- 
ness of the atmosphere at those parts. Dark spots are also occa- 
sionally seen in connection with the belts. 

In Fig. 105 are given two telescopic views of this planet ; the first, from 
a drawing by Sir John Herschel, as it appeared September 23d, 1832 ; the 

Questions. — b. Solar light and heat of Jupiter ? 253. Belts — how described? 254. 
Their cause ? a. What variations in appearance ? 



178 JUPITER. 

second, by Madler, in 1834. The two dark spots shown in the latter were 
employed- to determine the time of the planet's rotation. 

Fig. 105. 




TELESCOPIC VIEWS OF JUPITEB. 



b. Notwithstanding the cloudy masses with which the atmosphere 
appears to be charged, it is not thought that the latter has any very 
great height above the planet's surface ; for if such were the case the 
edges of the disc, instead of being sharply denned as we see them, 
would be nebulous and indistinct. 



SATELLITES OF JUPITER. 

255. The four satellites of Jupiter are among the most 
interesting bodies of the solar system. They were first seen 
by Galileo, in 1610, a short time after the invention of the 
telescope, and were perceived to be satellites by their appa- 
rent movements with respect to the planet, alternately 
approaching it, ^passing behind it, and receding from it; 
sometimes also passing over its disc and casting their 
shadows upon it. 

a. These planets have been distinguished by particular names, 

Questions. — 6. Atmosphere? 255. Satellites— by whom discorered? Their appa- 
rent motions ? a. How designated ? 



JUPITEK 179 

but are more generally designated by the numerals I., II., III., IV., 
according to their order from Jupiter. 

256. Their periodic times are, respectively, l d 18 h ; 3 d 
13 h ; 7 d 4 h ; and 16 d 16 h . The longest, it will be seen, is but 
a little more than half that of the moon. 

a. It will also be perceived that the second is very nearly twice the 
first ; and the third, twice the second. 

257. Their diameters in approximate numbers, are L, 2,300 
miles; II., 2,070 miles; III., 3,400 miles; IV., 2,900 miles; 
all, excepting the second, being larger than the moon 

a. These figures are based upon the measurements of their discs and 
a comparison of their apparent diameters with that of the planet as 
seen simultaneously. Thus, suppose the apparent diameter of Jupiter 
in opposition is found to be 45", and the third satellite is measured at 
If" ; the diameter of the satellite must then be -£- 6 - that of the primary 
planet, and 85,000 X jg = 3,400. 

6. As seen from Jupiter these bodies present quite large discs ; the 
apparent diameter of I. being 36' ; of II., 19' ; of III., 18' ; and of IV., 
9'. The first is therefore somewhat larger in appearance than that of 
the moon. The firmament of Jupiter must present a very beautiful 
diversity of phenomena. These various moons, all of which are occa- 
sionally above the horizon at one time, go through their phases within 
a few days ; the first within 42 hours. To an inhabitant of the first 
satellite, the apparent diameter of Jupiter must be 19° ; that is, about 
36 times as great as the moon ; while the amount of illuminated sur- 
face presented by it must be nearly 1300 times as great. 

c. Although their volumes are quite large, their masses are very 
inconsiderable, owing to their very small densities, which are I., -£-$ ; 
II., ^ ; III., tV ; IV., 2*5, the earth being 1. All are, thus, considerably 
lighter than water, and the first very much lighter than cork. 

258. Their distances from Jupiter are, respectively, 
264,000 miles, 423,000 miles, 678,000 miles, and 1,188,000 

miles. 

a. These are found by measuring their greatest elongations from 

Questions.— 256. Periodic times of the satellites ? 157. Their diameters ? a. How- 
found ? b. Apparent size at Jupiter? Apparent size of Jupiter at satellites? c. 
Masses and densities ? 253. Their distances from the primary ? a. How found? 



180 JUPITER. 

the planet, and comparing these with its apparent diameter. Thus, 
the greatest elongations are respectively, 136", 217", 349", and 611" ; 
the apparent equatorial diameter of the planet being 45". Dividing each 
elongation by 45", we find the ratio to the planet's diameter of the 
distances of the satellites respectively. These are nearly I., 3 ; II., 4.8 ; 
III., 7.7; IV., 13.6. Fig. 106 shows the comparative extent of these 
elongations. 

Pig. 106. 



JUPITER AND ITS SATELLITES AT THEIB GREATEST ELONGATIONS. 

b. The entire system of Jupiter is thus comprehended within a circular 
space of less than 2£ millions of miles in diameter, and subtends at its 
distance from the earth an angle less than 22', or about f the apparent 
diameter of the moon. A telescope, the field of view of which would 
include one-half the area of the moon's disc, would exhibit Jupiter and 
all his satellites, as represented in Fig. 106. 

c. A comparison of the periodic times and distances as above given 
will prove that they agree with Kepler's third law. Thus, taking I. 
and II. as an example, we find (ff) 2 =4.1 (nearly), and (|||) 3 = 4.1 
(nearly) ; hence, (85) 2 : (42) 2 : : (423,000) 3 : (264,000) 3 . 

259. The orbits of these bodies are almost circular, and 
very nearly in the plane of the planet's equator. They 
therefore make only a very small angle with the plane of its 
orbit (about 3°). 

260. The eclipses, occultations, and transits of the 
satellites present an endless series of interesting and useful 
phenomena ; and the situation of their orbits causes them 
to occur with very great frequency. 

a. I., II., and III. are eclipsed at every revolution ; but so peculiarly 
related to each other are their motions that their simultaneous eclipse 
is impossible. Laplace demonstrated that the mean longitude of I., 
plus twice that of III., minus three times that of II., is always equal to 

Questions.— b. Angular space covered by the system ? c. Kepler's law — how 
applied? 259. Figure and position of the orbits? 260. Eclipses? Why frequent? a. 
How many eclipses may occur at Jupiter during a Jovian year ? 



JUPITER, 



181 



180°. Hence, when two are eclipsed, the other must be on the oppo- 
site side of the planet. This is called the libration of the satellites. 
All four are, however, occasionally invisible, being concealed either 
behind or in front of the planet. This occurred last in August, 1867. It 
has been computed that, during a year of Jupiter, an inhabitant of the 
planet might behold 4,500 solar and lunar eclipses. 

b. During the transits the satellites appear like bright spots passing 
from east to west across the disc, preceded or followed by their shadows, 
which seem like small round dots as black as ink. 

Fig. 107. 





e ^y 



ECLIPSES, OCOTJLTATIONS, AND TRANSITS OF JUPITES'S SATELLITES. 

In Fig. 107, to an observer at E, I, is represented as eclipsed ; II., as just 
passing into the shadow of the planet ; III., just before a transit, the shadow 
preceding ; and IV., at the point of occultation. At E', I. has just passed behind 
the disc ; II. is in occultation ; III., a transit, both shadow and satellite being 
on the disc, the shadow preceding ; IV., just emerging from behind the 
planet ; at E", I. and II. are behind the disc, III. is in transit, but the 
shadow follows the satellite ; IV., just after an eclipse. 

261. Since the occurrence of these eclipses can be exactly 
predicted, they serve to mark points of absolute time ; so 
that if the precise moment at which they will occur at any 

Questions.— b. How do the satellites appear in a transit? 261. Why are these 
eclipses useful t 



182 SATUBK. 

particular place lias been computed, and the actual time of 
their occurrence at any other place is noted, a comparison 
of the two will give the difference of time, and, of course, 
the difference of longitude, between the two places. 

a. Thus, if a mariner perceives, by the nautical almanac, that the 
eclipse of a satellite will occur at 9 o'clock P.M., Washington time, 
and he notices that the eclipse does not take place till 11 o'clock P.M., 
he can infer that his position is 2 hours, or 30°, east of Washington. 

b. Velocity of Light found by the Eclipses of Jupiter's Sat- 
ellites. — In the prediction of these eclipses, a constant variation was for 
several years found to exist between the calculated and observed time 
of the occurrence, with this additional fact, that the eclipse was later 
as Jupiter receded from the earth and earlier as it approached the 
earth ; being about 16 m 35I 1 earlier in opposition than in conjunction. 
These observations were made by Olaus Roemer, a Danish astronomer ; 
and in 1675 he promulgated the theory, to account for the phenomena, 
that the passage of light from a luminous body is not instantaneous, 
but moves with a certain definite but immense velocity, requiring 16 m 
35£» to cross the earth's orbit. This theory has been universally 
accepted, and certain experiments recently made in France, by M. 
Fizeau and others, have confirmed it. The velocity of light must 
therefore be 184,000 miles a second. For 183,000,000 miles (distance 
across the earth's orbit) divided by 995£ (number of seconds in 16 m 
35^ s ), gives 184,000 (nearly). Light must therefore require 8£ min- 
utes to pass from the sun to the earth. So great a velocity is entirely 
inconceivable. 

III. SATURN h 

262. Satubk, the second of the major planets, is the 
centre of a very large and peculiar system, being attended 
by eight satellites and encompassed by several rings. It' 
shines with a dull yellowish light. 

a. Name and Sign.— Saturn, in the ancient mythology, was one of 
the older deities, and presided over time, the seasons, etc. He was 
represented as a very old man carrying a scythe in one hand. The 
sign of the planet is a rude representation of a scythe. 

Questions.— a. Illustration? b. What important discovery made by Roemer? In 
what way? What is the velocity of light ? 262. General description of Saturn? a. 
Name and sign ? 



SATURN. 183 

263. The aphelion distance of Saturn is about 921 mil- 
lions of miles ; the perihelion distance, 823 millions ; the 
mean distance being therefore 872 millions. 

a. This is nearly twice the distance of Jupiter, between which and 
Saturn there is a vast space of nearly 400 millions of miles, in linear 
breadth, through which there rolls no planetary body. Light requires 
about l^ k to pass from the sun to Saturn. 

264. The eccentricity of Saturn's orbit is nearly 50 
millions of miles, or about .056 of its mean distance, being 
but little greater, relatively, than that of Jupiter. 

265. The inclination of its oebit to the plane of the 
ecliptic is about 2}/ (2° 29' 36"). 

266. Its synodic period is 378 days (378.07 d ), and its 
sidereal period, 10,759 days or about 29^ years. 

a. For 378.07 J -r-365.25 d = 1.03514; and 378 07 d -^ .03514 = 10759 d 
(nearly). The year of Saturn contains, therefore, about 25,000 of its 
own days. 

267. The greatest apparent diameter of Saturn is 21" ; its 
least, 144". Its real equatorial diameter is about 74,000 miles. 

a. For the least distance from the earth is 823 millions of miles — 
93 millions = 730 millions : and the sine of 10£" is about .00005088, 
which being multiplied by 730,000,000 will give 37,000 (nearly)— the 
semi-diameter. 

268. The oblateness of Saturn is greater than that of 
any other planet, being a little more than j 1 ^ of its equatorial 
diameter, or 7,800 miles. 

a. Hence its polar diameter is only 66,200 miles ; its mean diame- 
ter being 70,100 miles. 

269. The axial rotation is performed in about 10.J 
hours (10 h 29 m 17 s ). 

a. This was the determination reached by Sir William Herschel by 

Questions. — 263. Distance from the sun ? a. Interval between Jupiter and Saturn ? 
264. Eccentricity? 265. Inclination of orbit? 266. Synodic and sidereal periods? 
a. How computed ? 26T. Apparent and real diameters ? 268. Oblateness ? 269. Time 
of rotation ? a. How and by whom found ? 



184 SATUEN. 

means of observations made on the belts which, like those of Jupiter, 
cross the planet's disc. Subsequent observations have indicated but 
little variation from it. 

b. The equatorial velocity of Saturn is, therefore, more than 22,000' 
miles an hour ; and as its density is very small, being only - a A r of the 
earth's, its oblateness should be, according to the law stated in Art. 

251, b, ( TqI ) X V- = 40^ ; that is, 40^ times as great as the earth's. 

But ^y X 40^ = - 6 & 9 L 8 = -1355 (nearly), or about -,- 5 -. So that its observed 
oblateness is much less than it ought to be in accordance with this law. 
The measurement of Saturn's apparent diameter is, however, so diffi- 
cult, in consequence of the rings, that there may be considerable error 
in the statement of its oblateness given above. 

c. Volume, Mass, and Density.— The volume of Saturn as com- 
pared with that of the earth, is (SVi^i 3 ) 3 = 695^ . ana its mass has been 
found to be 90 ; hence its density is (as above stated), 90 h- 695^ = ffr 
(nearly), the earth's being 1 ; or 5| X A =.726 as compared with 
water, which is somewhat lighter that oak wood. 

d. Superficial Gravity. — This must be, according to the figures 
above given, O&Wo) 2 X 90 =1.15 (nearly). Hence, a body at the sur- 
face of Saturn weighs only about \ more than at the surface of the 
earth, notwithstanding the immense size of that planet. 

270. The inclination of its axis toward the plane of 
its orbit is about 27° (26° 48' 40"), or a little greater than 
that of the earth. 

a. That is, its axis makes an angle of 27° with a perpendicular to its 
orbit. The angle which it makes with the plane of its orbit is 90° — 
27° = 63°. The position of the axis is such that its inclination toward 
the plane of the ecliptic is about 28° 10' ; and like that of the earth 
and those of the other planets, as far as it has been ascertained, the 
axis remains parallel to itself during the orbital motion. 

b. The Seasons of Saturn must therefore be similar to those of 
the earth, but like the year, 29^ times as long. 

c. Solar Light and Heat. — The distance of Saturn from the sun 

Questions. — b. How does the oblateness, computed by velocity and mass, compare 
with that found by observation? c. Volume, mass, and density ? d. Superficial grav- 
ity ? 270. Inclination of axis to the plane of its orbit ? a. To the plane of the ecliptic ? 
b. Seasons of Saturn? Solar light and heat? 



SATUKN. 185 

being more than 9 g times as great as the earth's, the apparent diameter 
of the sun must be less in the same proportion, or 82' -f- 9^ = 3' 22". 
Hence the light and heat, considered with reference to distance, must 
be, compared with the earth's, as (202"/ to (1920") 2 , or as 1 to (9.53) 2 ; 
that is, only - 9 L j- of the earth's. 

271. Satukn's Belts. — This planet, when viewed with a 
good telescope, appears to be encompassed with dusky belts ; 
but they are far more indistinct than those of Jupiter ; and 
instead of crossing the disc in straight lines like those of 
that body, they generally present a curved appearance, — an 
indication of the axial inclination. 

a. Sir William Herschel inferred the existence of a dense atmos- 
phere surrounding Saturn, both from the changes constantly occurring 
in the number and appearance of the belts, and the appearance of the 
satellites at the occurrence of occultations. The nearest was observed 
to cling to the edge of the disc about twenty minutes longer than 
would have been possible had there been no atmosphere to refract the 
light Indications of accumulations of ice and snow at the poles have 
also been detected, similar to those of Mars. 

272. Kings. — Saturn is encompassed by three or more 
thin, flat rings, all situated exactly or very nearly in the 
plane of its equator. 

a. History of their Discovery. — In his first telescopic examina- 
tion of this planet, Galileo noticed something peculiar in its form. As 
seen through his imperfect instrument, it appeared to him to have a 
small planet on each side ; and hence, he announced to Kepler the 
curious discovery that " Saturn was threefold ;" but continuing his 
observations, he saw, to his great astonishment, these companion 
bodies (as he thought) grow less and less, and finally disappear. For 
fifty years afterward the true cause of the appearance remained un 
known, the distortion of the planet's form being supposed to arise from 
two handles attached to it. Hence they were called ansa, the Latin 
word for handles. Huyghens, in 1659, discovered the real cause of the 
phenomenon, and announced it in these words : " The planet is sur- 
rounded by a slender, fiat ring, everywhere distinct from its surface, 

Questions.— 271. How do the belts appear ? a. What indications of an atmosphere ? 
272. What rings encompass Saturn ? a. History of their discovery ? 



186 SATURK. 

and inclined to the ecliptic." The division of the ring into two was 
discovered by an English astronomer in 1G85. We have now certain 
knowledge of the existence of three rings, and some indications of 
several more. 

273. Two of these rings are very distinctly observed, and 
are designated the interior and the exterior ring. The former 
is about 16,500 miles wide ; the latter, 10,000 miles. The 
distance of the interior ring from the planet is about 18,350 
miles ; and the interval between these rings, about 1,700 
miles. The thickness of the rings does not exceed 250 
miles, and may be much less. 

a. The diameter of the exterior ring, at the mean distance of the 
planet, subtends an angle of 40", and is, consequently, nearly 170,000 
miles. It will thus be evident that 1" of angular space at the distance 
of Saturn is equal to nearly 4,250 miles ; so that if the ring were 250 
miles in thickness, it would subtend only about - 2 V'« The difficulty of 
determining this precisely will at once be obvious. The mass of the 
ring has been computed to be equal to the 118th part of the planet's 
mass, from its effect in disturbing some of the satellites ; and this would 
prove, if its density is equal to that of the planet, that its thickness is 
about 140 miles. 

274. Within the interior ring there is a dusky or semi- 
transparent ring, having a crape-like appearance as it 
stretches across the bright disc of the planet. (See Fig. 108.) 

a. None of the early observers noticed this. In 1838, the Prussian 
astronomer, Galle, perceived a gradual shading off of the interior ring 
toward the planet. His announcement of the fact elicited no attention 
until, in 1850, the distinguished astronomer of our own country, 
G. P. Bond, plainly discovered and announced (Nov. 11) the existence 
of this dusky ring; before, however, the intelligence had reached 
England, the discovery had been made (Nov. 18) there also, by the 
celebrated observer, Dawes. The transparency of this ring was fully 
established in 1852 by Dawes and Lassell. There are also very decided 
indications that this dark ring is also double. 

Questions. —273. Principal rings — their dimensions? a. Diameter of exterior ring? 
Thickness of rings? 274. Dusky ring? a. History of its discovery? 



SATURN. 



187 



Fig. 108 shows the planet as seen by Dawes in 1852. The form and 
partial transparency of the dark ring are clearly represented ; the interval 

Fig- 108. 




TELESCOPIC VIEW OF SATXJBN. — DdlVCS. 

between the interior and exterior rings is also visible, as well as the line 
in the latter, supposed to indicate another division of the rings. 

b. Rotation of the Rings. — It was discovered by Sir William Her- 
schel, by observing certain bright spots seen on the surface of the rings, 
that they rotated on an axis perpendicular to their plane, and very nearly 
coincident with that of the planet. The time of rotation is about 10 h 
32 m , which is the time required by a satellite situated at a distance 
from the planet equal to the centre of the rings, to perform its revolu- 
tion, according to Kepler's third law. As the planet revolves around 
the sun, the rings constantly remain parallel to themselves. 

c. Stability of the Rings. — Observations of great delicacy have 
shown that the rings are not exactly concentric with the planet, the 
centre of gravity of the former revolving in a small orbit round that 
of the latter ; and Laplace showed that this is an essential condition 
of their stability ; since, if they were precisely concentric, a very slight 
disturbance, such as the attraction of a satellite, would be sufficient to 
destroy their equilibrium and finally precipitate them upon the planet. 

d. Physical Constitution of the Rings. — The rings are evidently 



Questions. — b. Rotation of the rings? c. Are the rings concentric with the planet? 
d. Why have the rings been supposed to he fluid ? What other hypothesis. 



188 SATURN. 

opaque, since they cast a shadow upon the planet and are in turn 
obscured by that of the planet itself ; and it was, until quite recently, 
thought that they consisted of solid matter. This, however, is now 
generally considered to be at variance both with theory and observa- 
tion ; it being shown that the equilibrium of solid rin^s could not long 
be preserved, except by an arrangement which certainly docs not 
exist. Moreover, several subordinate divisions have been remarked in 
the bright rings, portions of which are of a different shade, presenting the 
" appearance of four or five concentric and deepening bands," compared 
by Lassell to the " steps of an ampitheatre." These shaded bands and 
the lines which separate them do not always present exactly the same 
appearance. The idea has therefore been entertained that the rings 
might be fluid, not only from the circumstances above enumerated, but 
because minute observations disclose the fact that the rings have 
become broader and thinner than they were when first discovered. A 
more generally received hypothesis is, that the rings consist of vast 
numbers of satellites revolving around the planet ; and that being 
more sparsely scattered in the dark ring, they reflect the light im- 
perfectly and disclose the bright disc of the planet between them. 
This hypothesis not only explains all the phenomena of the rings, but 
is consistent with other phenomena presented by the solar system, to 
be referred to hereafter. 

275. Appearance of the Kings. — The rings, although 
circular, appear like ellipses because, being inclined to the 
plane of the ecliptic, they are always viewed obliquely. 
They become invisible when the dark side is turned toward 
the earth; and, when its edge only is presented, are seen, in 
very powerful telescopes, as a mere thread of light, cutting 
the disc of the planet. Sometimes the satellites appear along 
this thread like a series of brilliant beads on a string. 

a. The edge only of the rings is seen when their plane if prolonged 
would pass through the earth; also when the same plane passes 
through the sun, so that the edge only is illuminated. In each of 
these cases, the rings must disappear or present only a thread of 
light. They disappear also when their unillumined side is turned 

Questions.— 275. Appearance of the rings? When do they disappear? a. When 
is the edge only seen ? When is the dark side presented ? 



SATURN. 189 

toward the earth,, which must, of course, occur when their plane passes 
between the earth and sun, so that the rays of the latter fall only on 
that side of the rings which is turned away from the earth. 

Fig. 109. 




SATXJKN IN DIFFEBENT PABT8 OF ITS OKBIT. 

Fig. 109 represents Saturn in different parts of its orbit, the direction of 
the axis and the position of the plane of the rings constantly remaining the 
same. At A or E, the time of the planet's equinox, the plane of the rings 
passes through the sun, so that its edge only is illuminated, wherever the 
earth may be situated, which is to be conceived as revolving in a small 
orbit within that of Saturn. At the solstice C, the southern side of the 
rings is exhibited ; and at G, the northern side. At the intermediate points 
the rings are viewed obliquely. It will be obvious that, owing to the com- 
paratively small size of the earth's orbit, the plane of the rings can pass 
through the earth, or between it and the sun, only a short time before or 
after the equinox, and, as this must occur at each equinox, that the disap- 
pearance of the rings from this cause must occur twice during each sidereal 
revolution of the planet, or at intervals of 14| years. The last disappear- 
ance took place in 1862 , the next will occur in 1877. At the present time 
(1867), the northern surface of the rings is visible. 

276. Satellites. — Saturn is attended by eight satellites, 
seven of which reyolve very nearly in the plane of its 
equator, the orbit of the eighth, or most distant satellite, 
making with that plane an angle of 12|°. 

a. Names. —The names of these satellites in the order of their dis- 
tances from Saturn, beginning with the nearest, are the following : — 

Questions.— 276. How many satellites attend Saturn? The situation of their orhita? 
a. How named ? 



190 



SATURN. 



1. Mimas, 2. Enceladus, 3. Tethys, 4. Dio'ne, 5. Rhea, 6. Titan, 7. Hy- 
perion, and 8. Jap'etus. 

b. History of their Discovery. — Titan was discovered by Huy- 
gliens, in 1665 ; Tethys, Dione, Khea, and Japetus, by Cassini, within 
about twenty years afterward ; Mimas and Enceladus, by Sir William 
Herschel, in 1787 and 1789 ; and Hyperion was discovered by Lassell, at 
Liverpool, and by Bond, at Cambridge, Mass., on the same evening, 
September 19, 1848. 

c. The following are their periods and distances from the primary : 



DISTANCES. 



PEBIODS. 



DISTANCES. 



1. Mimas 

2. Enceladus 

3. Tethys 

4. Dione 



22|. 
Id 9h 
ld21h 
2 J 18- 



121,000 

155,000 
191,000 
246,000 



5. Khea 

6. Titan 

7. Hyperion 

8. Japetus 



4 12M, 
15 23. 

2U 7h 

791 8' 



343,000 

796,000 

1,006,000 

2,313,000 



277. The largest of the satellites is Titan, its diameter 
being 3,300 miles, which is larger than that of Mercury. 
The sizes of the others are very much less. 

a. That of Japetus is 1,800 miles ; Rhea, 1,200 ; Mimas ; 1,000 ; 
Tethys and Dione, 500 ; Enceladus and Hyperion, unknown. 

b. The orbit of Japetus subtends an angle of only 2H' ; so that this 
magnificent system of Saturn with his rings and eight satellites, at 
its immense distance from the earth, is contained within a space in the 
heavens less than one-half the disc of the moon. 

c. In 1862, while the ring was invisible, the rare phenomenon 
occurred of a transit of Titan across the disc of the primary. The 
shadow was observed by Dawes and others. The same phenomenon 
was observed by Sir William Herschel in 1789. 

d. The variations in the light of Titan indicated to Sir William 
Herschel an axial rotation of the satellite, which, like that of all other 
satellites whose periods have been discovered, is performed in the same 
time as the revolution around the primary. 

278. The celestial phenomena at Saturn must present 



Questions.— 6. History of their discovery ? c. Their periods and distances ? 277. 
Which is the largest satellite ? Its size ? a. Diameter of each of the other satellites ? 
6. Space in the heavens occupied by the Saturnian system ? c. Transit of Titan ? 278. 
Celestial phenomena at Saturn ? 



URANUS. 191 

a scene of extreme beauty and grandeur. The starry vault, 
besides being diversified by so many satellites, presenting 
every variety of phase, must be spanned, in certain parts of 
the planet, and during different portions of its long year, 
by broad, luminous arches, extending to different elevations, 
according to the place of the observer, and receiving upon 
their central parts the shadow of the planet. 

IV. URANUS, tf 

279. Uranus was discovered in 1781 by Sir William 
Herschel. It shines with a pale and faint light, and to the 
unassisted eye is scarcely distinguishable from the smallest 
of the visible stars. 

a. History of its Discovery. — This planet had been observed by- 
several astronomers previous to its discovery by Herschel, but had 
been mapped as a star at least twenty times between 1690 and 1771, 
its planetary character not having been discerned ; and even Herschel, 
on noticing that its appearance was different from that of a star, was 
not aware that he had discovered a new planet, but supposed it to be 
a comet, and so announced it to the world, April 19th, 1781. It was, 
however, in a few months, evident that the body was moving in an 
orbit much too circular for a comet ; but its planetary character, sug- 
gested first by Lexell, in June, 1781, was not fully established until 
1783, when Laplace partly calculated the elements of its orbit. This, 
however, does not detract from the merit of Herschel, in making this 
discovery ; for, the attention of astronomers having been called to this 
object, as one of a peculiar character, and not sidereal, it was a simple 
thing to determine whether it was a planet or a comet. The merit of 
the discovery consisted in that delicacy of observation, that skill in the 
use of instruments, and, more than all, that unfailing perseverance 
which characterized Herschel, and made him the great astronomer of 
his age. 

b. Name and Sign. — Herschel proposed to call the new planet 

Questions.— 279. When and by whom was Uranus discovered? Its appearance? 
a. History of its discovery ? b. Origin of the name and sign? 



192 URANUS. 

"Georgium Sidus," George's Star, in. compliment to his friend and 
patron, King George III. This name not being accepted by foreign 
astronomers, Lalande proposed to name it " Herschel," after its great 
discoverer ; and by this designation it was, for some time, quite gener- 
ally known. The scientific world has now definitely settled upon the 
name, suggested by Bode, of Uranus, which, in the Grecian mythology, 
was the name of the oldest of the deities, the father of Saturn, as 
Saturn was the father of Jupiter. The name of the discoverer is, 
however, partly connected with the planet by the sign, which is the 
letter H with a suspended orb. 

* 280. The aphelion distance of Uranus is about 1,836 
millions of miles ; its perihelion distance, 1,672 millions ; 
the mean distance being 1,754 millions, which is more than 
19 times (19.183) that of the earth. 

a. Light requires 2 hours 33 £ minutes to pass from the sun to 
Uranus ; for 8 m X 19.183 = 153.464 01 = 2 h 33^ m (nearly). Sunrise and 
sunset are therefore not perceived by the inhabitants of Uranus for 
two hours and a half after they really occur, for the light which pro- 
ceeds from the sun when it touches the plane of the horizon does not 
reach the eye until 2\ hours afterward. 

b. The distance of this planet from the sun is so vast that the 
greatest elongation of the earth as seen from it is only about 2°. That 
of Jupiter is only 16^°, while its apparent diameter is but little greater 
than that of Mercury as seen from the earth. Even Saturn departs 
only about 29° from the sun, its apparent diameter being less than 20". 
The inhabitants of the planet, if any there be, must therefore possess 
much less opportunity than ourselves to become acquainted with the 
constituent members of the great system to which they belong. 

281. The eccentricity of the orbit of Uranus is' about 
82 millions of miles, or about .047 of its mean distance. 

282. The inclination of its orbit is less than that of 
any other planet, being only 46^'. 

Questions. — 280. What is its distance from the sun ? a. What time does light 
require to pass from the sun to Uranus ? Effect on apparent sunrise and sunset ? b. 
Elongations and apparent diameters of the planets as seen from Uranus ? 281. Eccen- 
tricity of its orbit ? 282. Inclination of its orbit ? 



URANUS. 193 

a. Nevertheless, so vast is its distance that, at its greatest latitude, 
it may depart from the plane of the ecliptic more than 24 millions of 
miles. 

283. Its synodic period is 369.6 days; and therefore 
its sidereal period is 30,687 days, or about 84 years. 

a* The computation may be made as in the case of the other planets : 
369.6 -5- 365.25 = 1.0119 ; that is, Uranus performs only .0119 of a side- 
real revolution during one of the earth. Therefore, 365.25 d -i-. 0119= 
30,687 d , the sidereal period. 

b. In the case of a very distant planet, the sidereal period may be 
readily found by observing the daily arc of movement of the planet 
when in quadrature : for, at that time, the line joining the earth" and 
planet is a tangent to the earth's orbit (see Fig 28), so that, for a short 
time, the earth moves either toward or from the planet, and does not 
affect the apparent motion of the latter , while its distance is so great 
that its geocentric increase in longitude is almost equal to its helio- 
centric. Now, the apparent daily increase of the longitude of Uranus 
in quadrature is 42.23", and 360° -s- 42.23" = 30,689, which gives a 
near approximation to the true sidereal period. 

284. The greatest apparent diameter of Uranus is about 
4" ; and as 1", at the least distance of this planet, subtends 
8,350 miles, the real diameter must be 33,400 miles. (By 
more exact calculations, it is found to be 33,247 miles.) 

a. The oblateness has not positively been ascertained. Madler esti- 
mates it to be as much as -fe. The tolume of Uranus is abqut 72^ times 
that of the earth ; but its mass is only 13 times ; hence its density is 
less than ^ that of the earth, or about equal to that of water. 

285. As the disc of Uranus presents neither belts nor 
spots, the period of its rotation and its axial inclination still 
remain unknown. It is thought, from the positions of the 
orbits of the satellites, that the inclination of its axis is 

Questions. — a. Possible distance from the plane of the ecliptic ? 283. Synodic and 
6idereal periods ? a. How calculated? b. How may the sidereal period be found by 
the daily increment of longitude? 284. Apparent and real diameter of Uranus ? a. 
Oblateness ? Volume ? Mass ? Density ? 285. Diurnal rotation ? 



194 



NEPTUNE. 



very great ; and analogy would lead us to believe that its 
diurnal period is nearly the same as that of Jupiter or 
Saturn. 

286. Satellites.— Uranus is known to be attended by 
four satelites, which differ from all the other planets of the 
solar system, by revolving in their orbits from east to west. 

a. History of their Discovery. — Sir William Herschel, in 1787, 
discovered the third and fourth satellites, and subsequently announced 
the discovery of four more ; the first two of these are all that later 
astronomers have been able to find, although every effort has been 
made with the best instruments to detect the others. In 1847 two others, 
situated within the orbit of the nearest discovered by Herschel, were 
detected, oue by Lassell and the other by O. Struve. 

b. The following are the names of these satellites, with their periods 
and distances : 



1 

1 PEBIODS. 


DISTANCES. 




FEBIODS. 


DISTANCES. 


1. Aeikl 

2. Umbeiel 


2d 12-Jh 
4-1 3|h 


123,000 
171,000 


3. TlTANIA 

4. Obebon 


8dl?h 
13J 17»> 


281,000 
376,000 



c. Their orbits are inclined to the plane of that of the primary at 
an angle of 79° ; but, as their motion is retrograde, it seems probable 
that the poles have been reversed in position, the south pole being 
north of the ecliptic, and vice versa. The inclination is properly, there- 
fore, 101°. 



V. NEPTUNE f 

287. Neptune is the most distant planet known to belong 
to the solar system. It was first observed in 1846 by Dr. Galle 
at Berlin ; but its existence had been predicted, and its posi- 
tion in the heavens very nearly ascertained by the calculations 
of M. Leverrier, in France, and Mr. Adams, in England ; 
these calculations being based upon certain observed irregu- 
larities in the motion of Uranus. 

Questions. — 286. How many satellites attend Uranus? Direction of their orbital 
motion ? a. History of their discovery ? b. Names, periods, and distances ? c. Posi- 
tion of their orbits and poles ? 287. By whom, and how was Neptune discovered ? 



NEPTUNE. 195 

a. History of its Discovery. — The discovery of this planet was 
one of the proudest achievements of mathematical science in itsappli> 
cation to astronomy, and afforded a more striking proof of the truth of 
the great ] aw of universal gravitation than had previously been ascer- 
tained. After the discovery of Uranus, in 1781, it was ascertained that 
the planet had several times been observed by astronomers, and its 
place recorded as a star. These positions of the planet could not, 
however, be reconciled with those recorded after its actual discovery ; 
and observation soon showed that its motion was at certain points 
increased, and at others diminished, by some force acting beyond it 
and in the plane of its orbit. These facts suggested the existence of 
another planet, revolving in an orbit exterior to that of Uranus, and, 
according to Bode's law, extending nearly twice as far from the sun. 
Adams and Leverrier almost simultaneously undertook to find, by 
mathematical analysis, where this planet must be in order to produce 
these perturbations. The former reached the solution of this wonder- 
ful problem first, and, in October, 1845, after three years of toil, 
communicated to Mr. Airy, Astronomer Royal, the result, pointing out 
the position of the planet and the elements of its orbit. The search 
for the planet was not, however, commenced until Leverrier published 
the result of his labors, which was found to agree so closely with that 
attained by Adams, that astronomers both in France and England 
prepared to construct maps of the part of the heavens indicated, in 
order to detect the planet. 

In this they were anticipated by the Berlin observer, who, being 
informed by Leverrier of the result of his computations, and having 
by a fortunate coincidence just received a newly prepared star-map of 
the 21st hour of right ascension (the part of the heavens designated by 
Leverrier), immediately compared it with the stars, and found one of 
them missing. The observations of the following evening, by detect- 
ing a retrograde motion of this star, established its true character. It 
was the planet sought for, and, wonderful to relate, was found only 
52' from the place assigned by Leverrier. He had also stated its appa- 
rent diameter at 3.3'" ; it was found by actual measurement to be 3". 
Adams's determination of the place of the supposed planet differed 
from the true place by about 2°. 

b. Name and Sign. — This planet, according to the system of 
mythological designations, was, after considerable discussion, called 

Questions.— a. Circumstances connected with its discovery ? How nearly was. its 
true place predicted ? h. Name and sign ? 



196 ' NEPTUNE. 

Neptune. The sign is the head of a trident — the peculiar symbol of 
this deity. 

288. The aphelion distance of Neptune is 2,770 mil- 
lions of miles ; its perihelion distance, 2,722 millions ; its 
mean distance being 2,746 millions. 

a. This is about 30 times the distance of the earth ; but according 
to Bode's law, it should have been 38.8 times ; so that this remarkable 
relation of the planets, failing in this instance, ceases to be a law, and 
becomes, apparently, only a curious coincidence. 

b. So immense is the distance of Neptune that only Saturn and 
Uranus can be seen from it. If there are astronomers, however, on the 
planet, they must have much better opportunities than ourselves for 
becoming acquainted with the distances of the stars ; since, at oppo- 
site periods of their long year, they are situated at positions in space 
about 5.500 millions of miles apart. 

e. Since the distance of Neptune from the sun is 30 times that of 
the earth, light requires 8 m X 30 == 4 h , to reach that planet. 

289. The eccentricity of the orbit of Neptune is about 
24 millions of miles, which is only .0087 of its mean dis- 
tance ; so that it is, relatively, but little more than one-half 
that of the earth's orbit. 

290. The inclination of its orbit to the plane of the 
ecliptic is very small, being only If ° (1° 47'). 

a* The sine of 1° 47' is .031 ; hence Neptune, when at its mean dis- 
tance from the sun, and at the point of greatest latitude north or south 
of the ecliptic, must be more than 85 millions of miles from the plane 
of that circle ; for, 2.746,000,C00 X .031 = 85,126,000. 

291. Its synodic period is about 367^ days (367.46875) ; 
hence its sidereal period is 60,127 days, or about 164.; 
years. 

a. It is more difficult to calculate the sidereal periods of these 

Questions.— 288. Aphelion, perihelion, and mean distances? a. Does it agree with 
Bode's law ? 6. Which planets can he seen at Neptune ? c. How long does light 
require to pass from the sun to Neptune? 289. Eccentricity of its orbit? 290. Incli- 
nation ? a. How far may it depart from the plane of the ecliptic? How is this calcu- 
lated? 291. Synodic period ? Sidereal period ? a. How calculated ? 



KEPTUXE. 197 

remote planets ; since the synodic period is so nearly equal to the side 
real period of the earth, that the fraction of a revolution performed 
during the latter is very small. In the case of Neptune it is a little 
over .0060746 ; that is, 367.46875 -h 365.25 = 1.0060746 -f ; and 365.25 
-r- .0060746 = 60,127 days (nearly). 

292. The appakent diameter of Neptune when greatest 
is 2.9" ; hence its real diameter must be nearly 37,000 miles. 

a. For the least distance of Neptune from the earth is 2,722 millions 
— 93 millions = 2,629 millions ; now the sine of 2.9" is .000014 ; and 
2,629 millions multiplied by this small fraction will give 36,806 miles. 

b. Volume, Mass, and Density.— The volume of Neptune, if cal- 
culated by the method previously explained, will be found to be very 
nearly 99 times as great as that of the earth, and consequently is only 
about iV as large as Jupiter. Its mass is nearly 17 times (16.76) as 
great as the earth's [Prof, Pierce] ; consequently its density must be 
about £ that of the earth, or somewhat more than ■§$ as heavy as water. 

c. Solar Light and Heat. —The apparent diameter of the sun as 
seen at Neptune must be a little more thanl' ; for, 32' -5- 30.037 (ratio of 
of Neptune's distance to the earth's) — 64"(nearly). Hence, the sun at this 
planet looks but little larger than Venus ; but its light is vastly more 
brilliant. For, since the intensity of light varies inversely as the 
square of the distance, and (30.037) 2 = 902 (nearly), the light at Nep- 
tune must be ■$* of that at the earth, and hence is nearly equal to 
that of 670 full moons (157, 6> This is probably as great as that 
which would be produced by 20,000 stars shining at once in the firma- 
ment, each equal to Venus when its splendor is greatest. 

293. A satellite of this planet was discovered by Lassell 
in October, 1846, and was afterward observed by several 
other astronomers. 

«. From observations made about the same time the existence of 
another satellite was suspected, as well as a ring analogous to that of 
Saturn ; but the most diligent and careful scrutiny with very powerful 
telescopes has failed to detect any indications of the truth of these 
conjectures. 

Questions.— 292. Apparent diameter of Neptune ? Its real diameter ? a. How- 
found ? 6. Its volume, mass, and density? c. How great is the intensity of solar 
light and heat? How found? 293. By whom and when was the satellite discovered ? 
o. What conjectures as to another satellite, etc. ? 



L98 NEPTUNE: 

b. Distance of the Satellite. — The observations made by eminent 
astronomers (principally those of M. Struve, Mr, Lassell, and Mr. 
Bmd) have shown that the greatest elongation of the satellite from 
its primary is 18", the apparent diameter of the latter being at the 
same time 2.8". Hence its distance must be 18" -+- 2.8" = 6f diame- 
ters, or 12 £ radii, of the planet ; and 18,500 X 12f =238,000 miles, or 
about the same as the moon's distance from the earth. 

c. Inclination, Period, and Rotation. — The orbit of this satellite is 
nearly circular, and is inclined to the orbit of Neptune in an angle of 
29° Its motion, like that of the satellites of Uranus, is retrograde, or 
from east to west. Its sidereal period, as determined by Lassell at Malta, 
in 1852, is 5 d 21 h . Periodical changes in its brightness were observed 
by Lassell, which indicated that this satellite, like others in the sys- 
tem, rotates on its axis in the same time that it revolves around its 
primary. 

d. Are there Planets beyond Neptune? — This is a question 
which we are at present entirely unable to answer. Future genera- 
tions may, with greater resources of science and mechanical skill, 
disclose new marvels in our system, and detect other bodies obedient 
to the dominion of its great central sun. The nearest of the stars is 
known to be nearly 7,000 times as far from Neptune as that body is 
from the sun ; and it is by no means improbable, therefore, that so 
vast a space should contain planetary bodies reached by the solar 
attraction, but very far beyond the sphere of any other central lumi- 
nary. It will require, however, far greater means than we possess to 
bring this to a practical determination. 

Questions.— b. What is the distance of this satellite from the primary? How cal- 
culated ? c. Its inclination of orbit ? Orbital revolution — period and direction ? Axial 
rotation ? d. is Neptune the remotest planet ? 






CHAPTER XIV. 



THE MINOR PLANETS, OR ASTEROIDS. 

294. The minor planets are a large number of small 
bodies revolving around the sun between the orbits of Mars 
and Jupiter. The number discovered up to the present 
time (1867) is 95. 

a. Discovery of Ceres and Pallas. — The existence of so large an 
interval between Mars and Jupiter, compared with the relative dis- 
tances of the other planets, for a long time engaged the attention and 
incited the researches of astronomers. Kepler conjectured that a 
planet existed in this part of the system, too small to be detected ; and 
this opinion received considerable support from the publication of 
Bode's law in 1772. When Uranus was discovered, in 1781, and its 
distance was found to conform to this law, the German astronomers 
became so confident of the truth of this bold conjecture of Kepler, that, 
in 1800, they formed, under the leadership of Baron de Zach, an asso- 
ciation of 24 observers to divide the zodiac into sections and make a 
thorough search for the supposed planet. This systematic exploration 
had, however, been scarcely commenced, when, in 1801, Piazzi, an 
Italian astronomer, while engaged in constructing a catalogue of stars, 
detected a new planet. It was called by him Ceres. In the next year, 
while looking for the new planet, Olbers discovered another, which he 
called Pallas. 

b. Discovery of Juno and Vesta — Theory of Olbers. — The ex- 
treme minuteness of the new planets, and the near approach of their 
orbits at the nodes, led Olbers to suppose that they might be the frag- 
ments of a much larger planet once revolving in this part of the 
system, and shattered by some extraordinary convulsion. Believing 

Questions.— 294 "What are the minor planets? Their number? a. How and by 
whom were Ceres and Pallas discovered ? b. Juno and Vesta ? Theory of Olbers? 



200 MIKOE PLACETS. 

tliat other fragments existed, and that they must pass near the nodes 
of those already found, he resolved to search carefully in the direction 
of those points ; but while he was thus engaged, Harding, of the 
observatory of Lilienthal, discovered, in 1804, very near one of those 
points, a third planet, which he called Juno. Olbers, still further stim- 
ulated by this event to continue the investigation which he had 
commenced, was at length, in 1807, rewarded by discovering a fourth 
planet, Vesta, near the opposite node. From this date until 1845, no 
additional discovery was made. These small planets were called 
Asteroids by Herschel, from their resemblance, in appearance, to stars. 

c. Discovery of the other Minor Planets. — In 1845, M. Hencke, 
an amateur astronomer of Driessen, after a series of observations con- 
tinued for fifteen years with the use of the Berlin star-maps, discovered 
Astrcea, the fifth of this singular zone of telescopic planets. The 
others have been discovered in the following order : In 1847, Hebe, 
Iris, Flora; 1848, Metis; 1849, JSygeia ; 1850, Parthen'ope, Victoria, 
and Egeria ; 1851, Ire'ne and Eunomia; 1852, Psyche, Thetis, Mel- 
pom' ene, Fortu'na, Massilia, Lutetia, Colli' ope, and Thali'a; 1853, 
Themis, Phoce'a Proserpina, and Enter' pe ; 1854, BeUo'na, Amphi- 
tri'te, Urania, Euphros'yne, Porno' na, and Polyhym'nia ; 1855, Circe, 
Leuco'thea, Atalan'ta, and Fi'des ; 1856, Le'da, Lcetita, Harmonia, 
Daph'ne, and Isis ; 1857, Ariad'ne, Ny'sa, Euge'nia, Hestia, Mel'ete, 
Aglai'a, Boris, Pa'les, and Virginia; 1858, Neman' sa, Euro' pa, Ca- 
lypso, Alexandra, and Pando'ra; 1859, Mnemosyne; 1860, Concordia, 
Darfae, Olympia, Era'to, and Echo ; 1861, Ausonia, Angeli'na, Cpb'ele, 
Ma'ia, Asia, Hesperia, Leto, Panope'a, Feronia, and M'obe; 1862, 
Clfi'ie, Oalate'a, Euryd'ice, Fre'ia, and Frig'ga; 1863, Diana and 
Euryn'ome; 1864, Sappho, Terpsich' ore, and Alcmene; 1865, Beatrix, 
Clio, and Io ; 1866, Sem'ele, Sylvia, This be, <§), Anti'ope, © ; 1867, <§> 
(§), <§>, ©. The largest number discovered in any single year is ten 
(in 1861) ; and in the three years, '52, '57, and '61, no less that 27 were 
discovered. 

d. Names of the Discoverers.— Dr. Luther, at the observatory of 
Bilk, near Dusseldorf, has discovered no less than 16, and is at the 
head of planet discoverers; Mr. Herman Goldschmidt, an amateur 

QrasTiONS.— c. "What time elapsed before Astrasa was discovered? Mention those 
discovered in each subsequent year. In what year were the largest number discov- 
ered? Who has discovered the greatest number? d. What other discoverers are 
named ? How many of the minor planets were discovered in the United States ? How 
are these bodies designated ? 



MINOR PLANETS. 201 

astronomer of Paris, has discovered 14; Mr. Hind, a distinguished 
English astronomer, 10 ; Be Gasparis, at Naples, 9 ; M. Chacornac, at 
Marseilles and Paris, 6 ; Mr. Pogson, an English astronomer, 6 (3 at 
Oxford, and 3 at Madras) • Br. G. H. F. Peters, at Clinton, N. Y., 6 ; 
M. Tempel, at Marseilles, 4 ; Mr. Ferguson, at Washington, 3 ; Mr. Wat- 
son, at Ann Arbor, Michigan, 3 ; Mr. Tuttle, at Cambridge, Mass., 2 ; 
several other observers, 1 or 2 each. Fifteen of these planets have 
been discovered in this country. Instead of the names above given, 
the minor planets are now generally distinguished by numerals accord- 
ing to the order of their discovery. Several of these bodies were dis- 
covered by two or more observers independently. 

295. The average distance of these planets from the 
sun is about 260 millions of miles. That of the nearest, 
Flora, is about 201 millions ; that of the most distant, 
Sylvia, is nearly 320 millions. The entire width of the zone 
in which they revolve is, however, about 190 millions of miles. 

296. The inclination of their orbits is very diverse ; 
more than one-third of the whole have a greater inclination 
than 8°, and consequently extend beyond the zodiac. The 
greatest is that of Pallas, amounting to 34° 42' ; the least, 
that of Massilia, which is only 41'. 

297. The eccentricity of their orbits is equally variable ; 
the most eccentric being that of Polyhymnia, which is 
.337, or more than one-third ; the least eccentric is that of 
Europa, which is only .004, or ^1-q. 

a. These orbits are not concentric ; but if represented on a plane 
surface, would appear to cross each other, so as to give the idea of 
constant and inevitable collisions. " If," says D' Arrest, of Copenhagen, 
" these orbits were figured under the form of material rings, these rings 
would be found so entangled, that it would be possible, by means of 
one among them taken at a hazard, to lift up all the rest." The orbits 
do not, however, actually intersect each other, because they are situ- 
ated in different planes ; but some of them approach within very short 

Questions.— 295. Average distance? Which is the nearest? The farthest? 296. 
Inclination of their orhits? How many heyond the zodiac? The most inclined? The 
least ? 297. Eccentricity ? Greatest ? Least ? a. Position of their orbits ? 



202 MINOR PLANETS. 

distances of each other. The orbit of Fortuna, for example, approaches 
the orbit of Metis within less than the moon's distance from the earth. 
This is also true of the orbits of Astraea and Massilia, and those of 
Lutetia and Juno. 

298. The largest of the minor planets is Pallas, the 
diameter of which is variously estimated at from 300 to 700 
miles. These bodies are generally so small that it is quite 
impossible to measure their apparent diameters, or to say 
which is the smallest. The brightest of these planets is 
Vesta ; the faintest, Atalanta. Vesta, Ceres, and Pallas 
have been seen with the naked eye, having the appearance 
of very small stars. 

299. The sidereal period of Flora is 3j years ; that 
of Sylvia is about 6^ years. The average period of the 
whole is about 44 years. 

a. Origin of the Minor Planets. — The theory of Gibers has 
already been alluded to ; it supposes that these little planets are the 
fragments of a much larger one, which by an extraordinary catastro- 
phe was, in remote antiquity, shivered to pieces. Prof. Alexander 
has endeavored to compute the size and form of this planet. He sup- 
poses that it was not of the form of a globe, but shaped like a lens 
or wafer, the equatorial and polar diameters being respectively, 70,000 
miles and 8 miles ; that the time of its rotation was about 3^ days; 
and that it burst in consequence of its great velocity, as grindstones 
and fly-wheels sometimes do. This theory of an exploded planet has 
not been generally accepted, since it is highly improbable, and sup- 
ported by no analogous facts. 

6. Nebular Hypothesis. — This was invented by Laplace to account 
for the formation of the solar system by the operation of ordinary 
physical laws. He conceived that the matter of which the various 
bodies belonging to this system are composed, originally had an enor- 
mously high temperature and existed in the condition of gas or vapor, 
filling a vast space ; that as this mass cooled, and, of course, unequally, 
currents were formed within it, which, tending to different points or 



Questions.— 298. Which is the largest of the planets ? The brightest ? The faintest ? 
290. Average sidereal period ? Longest? Shortest? a. Origin of the minor planets ? 
Asteroid planet ? 6. Nebular hypothesis? 



MIXOlt PLACETS. 203 

centres, gave it finally a slow rotation ; that this increased by degrees, 
until the centrifugal force exceeded the attraction of the central mass, 
and a zone or ring became detached, of a lower temperature, but still 
vaporous or liquid ; and that thus successive rings were formed, which 
breaking up as they rotated, the parts finally came together and 
formed spheroidal masses revolving around the original mass. If these 
rings condensed without breaking up they would continue to revolve 
as rings, like those of Saturn ; if, on the other hand, they broke up 
into small parts, none sufficiently large to attract all the others, they 
would condense into fragments and continue to revolve as small 
planets, like the asteroids. The larger planet masses, being still in a 
vaporous condition, would, as they cooled and condensed, throw off 
rings like the original mass , and in this manner either satellites or rings 
would be formed. The residue of the original nebulous mass he con- 
ceived to be the sun. 

Such is a brief outline of this celebrated and most ingenious 
hypothesis, — an hypothesis which every subsequent discovery has 
seemed to harmonize with and confirm. Whatever theory be adopted 
to account for the development of the solar system and the exist- 
ence of this zone of small planets, it must not be forgotten that the 
infinite power and intelligence of the Great Creator could alone 
have brought them into being. The only question is, in what way did 
He exert this power, and in what manner did He ordain that all these 
wonderful orbs should come into existence as witnesses of His omnipo- 
tence and benevolent design. 

c. Decrease in Brightness of the Successive Groups. — The 
brightest of the minor planets seem to have been discovered, for each 
successive group is less conspicuous than those preceding it. The 
first ten resemble stars of the eighth magnitude [the brightest stars 
are of the first] ; the last ten are but little brighter than stars of the 
twelfth magnitude. It is not anticipated, therefore, that others will 
hereafter be detected with the readiness and frequency which have 
marked the discoveries of the last ten years. The labor required in 
the discovery of these little bodies is almost inconceivable. The 
most successful discoverers have attained the object of their efforts 
only after mapping down every minute star in certain zones of the 
heavens ; and to do this required a patient and toilsome watching 
during every clear night for many months. 

Questions. — e. What decrease in brightness is referred to ? Difficulties in discover- 
ing these bodies ? 



CHAPTER XV. 

MUTUAL ATTRACTIONS OF THE PLANETS. 

300. The planets, while revolving around the sun, 
constantly disturb each other's motions, and thus give rise 
to numerous irregularities, similar to those which take 
place in the revolution of the moon around the earth. 

301. These irregularities are called inequalities or per- 
turbations. They are either periodic or secular, the former 
requiring short, the latter very long periods of time for their 
completion. 

a. Problem of the Three Bodies. — To compute the exact place 
of a planet at any time requires that all the inequalities due to the 
disturbing action of other planets should he taken into account ; and 
to do this has tasked to the utmost the highest powers of the human 
intellect. The problem is, however, simplified by the fact that, as the 
sun's attraction is so much greater than that of the other bodies, the 
place of the planet can be found by first supposing that it revolves in 
an exact elliptical orbit, and then calculating the amount of disturbance 
due to each other planet in succession ; the aggregate of the results 
thus obtained giving the proper correction to be applied in order to 
ascertain the true place. This has been called the The Problem of the 
Three Bodies, because it involves the investigation of the motion of 
one body revolving around another, and continually disturbed by the 
attraction of a third. To determine, therefore, all the inequalities to 
which any planet is subject, it is necessary to solve this problem sepa- 
rately for every other planet by which it may be disturbed. Its 
complete solution surpasses the powers of the most skillful mathe- 
matician. 



Questions.— 300. How do the planets disturb each other ? 301. What are the irregu- 
larities called ? Of how many kinds ? a. What is the " Problem of the Three Bodies ?" 



ATTRACTIONS OF THE PLANETS. 205 

302. The elements of a planet's orbit are the facts 
which it is necessary to know in order to determine the pre- 
cise situation of the planet at any instant. They are — 1. 
The position of the line of nodes ; 2. The inclination of the 
orbit to the plane of the ecliptic ; 3. The place of the peri- 
helion ; 4. The eccentricity ; 5. The major axis. 

a. Elements 1, 2, and 3 determine the position of the orbit ; 4, its 
figure ; and 5, its size. In order to find the place of the planet, it is 
necessary also to know the periodic time, and the place of the planet at 
any particular epoch. 

b. Heliocentric and Geocentric Place. — The true position of a 
planet is that in which it would appear to be situated if viewed from 
the sun, that is, its heliocentric place ; hence, one important point in 
ascertaining a planet's true position is to deduce its heliocentric place 
from its geocentric place, or situation as seen from the earth. 

303. The only invariable element is the length of the 
major axis ; every other, in the case of each planet, under- 
goes certain small changes, such as those which have been 
described in the orbits and motions of the earth and moon. 

a. Thus the inclinations of the orbits of Mercury, Venus, and 
Uranus are increasing ; those of Mars, Jupiter, and Saturn are dimin- 
ishing ; the greatest variation being that of Jupiter, which is 23" in a 
century. A similar variation occurs in the positions of the nodes and 
perihelion, and in the amount of eccentricity. In the case of the earth, 
as has been stated (Art. 125, e), the latter is diminishing ; and this is 
also true of Venus, Saturn, and Uranus ; while that of Mercury, Mars, 
and Jupiter is increasing. The greatest variation is that of Saturn, 
which is about .00031 of its mean distance in a century. This is rela- 
tively about 7i times as great as that of the earth, and amounts 
absolutely to about 2,700 miles a year; while the absolute annual 
variation of the earth's eccentricity is only 36£ miles. All these 
changes are confined within certain very narrow limits, after reaching 
which they occur in an opposite direction. 



Questions.— 302. What are the elements of a planet's orbit ? a. What is determined 
by them ? What else must be known to determine a planet's place ? b. What is meant 
by the heliocentric and geocentric places of a planet ? 203. Which element isinvariable? 
a. What examples are given of variable elements? 



206 ATTRACTIONS OF THE PLANETS. 

304. The motions of the planets are retarded or 
accelerated by their mutual attractions, according to their 
positions with respect to each other and to the sun ; but as 
action and reaction are equal and in opposite directions, 
whenever one is accelerated the other which acts upon it 
must be retarded. 

Thus, in Fig. 93, page 151, the planet at M must have its motion accel- 
erated by that of the earth at E, while the latter must be retarded ; but the 
acceleration of M is greater than the retardation of E, because the disturb- 
ing force at M acts more nearly in the direction of the planet's motion. 
After conjunction this is reversed ; the motion of the earth being accelerated 
and that of the planet retarded. 

a. If the planets' orbits were exactly circular, the amount of accel- 
eration in one part of the orbit would be counterbalanced by the 
retardation in the other, and the inequalities would, in a synodic 
period, cancel each other : but as the oi-bits are elliptical, the successive 
conjunctions must occur at different parts of the orbits, where the plan- 
ets are at different distances from each other; so that the inequalities 
must increase while the conjunctions occur in one part of the orbit, 
and diminish while they take place in the other. If the conjunctions 
always occurred in the same part of the orbit, the inequalities would 
constantly accumulate, and the system would be destroyed. This is 
nearly the case with Jupiter and Saturn. 

b. Great Inequality of Jupiter and Saturn. — The periodic times 
of Jupiter and Saturn are respectively 4,332 days and 10,759 days ; and 
hence, 5 of the former are nearly equal to 2 of the latter ; so that, in 5 
revolutions of Jupiter, or about 59 of our years, the conjunctions take 
place at nearly the same points of their orbits. The synodic period of 
these two planets is 19.86 years ; and during the 17th and 18th cen- 
turies the conjunctions constantly occurred almost at their points 
of nearest approach to each other, so that Jupiter's period appeared to 
be shortened and Saturn's lengthened, greatly to the perplexity of 
astronomers, till Laplace demonstrated the cause. Similar coincidences 
exist in the periods of Venus *nd the earth, but the disturbance accu- 
mulates only for a short period. It will be obvious, therefore, that the 



Questions.— 304. How are the motions of the planets accelerated or retarded? a. 
EffWt, in circular orhits ? In elliptical orbits i b. Great inequality of Jupiter and 
Saturn — what is meant by it? 



ATTRACTIONS OF THE PLANETS. 207 

stability of the system depends on the orbits' being circular, or the 
periods' being incommensurable. 

305. Since the attraction of gravitation is reciprocal, the 
sun is attracted by the planets, and each primary planet is 
attracted by its satellites ; and, therefore, instead of revolv- 
ing one around the other as a centre, they in fact revolve 
around their common centre of gravity. 

a. By the centre of gravity of two or more bodies connected together 
in any way, is meant the point around which they all balance each 
other. The centre of gravity of the solar system moves in a small 
and very irregular orbit, since it results from the joint action of all the 
planets Its distance from the centre of the sun can never be equal to 
the diameter of the latter ; and within this limit the centre of the sun 
mast revolve around it. 

306. Masses of the Planets.— The amount of attrac- 
tion exerted by one body upon another is an exact measure 
of its mass. The masses of the planets that are attended 
by satellites are found by comparing the attraction of the 
sun upon the planets, with the attraction which they exert 
themselves upon their satellites. The masses of the planets 
not attended by satellites are found by ascertaining the 
amount of disturbance which they occasion in the motions 
of bodies in their vicinity. 

a. Comparative Masses of the Sun and Planets.— To determine 
these it will be most convenient to resort to simple algebraic represen- 
tation. Let M be the mass of the sun, and m that of the earth ; F and 
/, their respective forces of attraction, P and p, their periodic times, 
and D and d, their distances. Then, according to the law of gravita- 
tion, the ratio of the attractions is equal to the direct ratio of the 
masses multiplied by the inverse ratio of the squares of the distances. 

rpw . F M d 2 , /_. ... _ d?\ M F 

That is, -, = — X ™ ; hence, ( dividing by — 2 1 we have — = - x 

Questions.— 305. Do the planets revolve around the sun as a centre ? a. What is 
meant by the centre of gravity ? What is the shape and magnitude of the sun's orbit, 
and the orbit of the centre of gravity? 306. What is the general method of determin- 
ing the masses of the planets ? a. How to find the comparative masses of the sun and 
pian^ts ? What calculation is made for the sun and earth ? The earth and Saturn ? 



208 ATTRACTIONS OF THE PLANETS, 

D 3 

-p . But it can be shown by simple geometry that the forces are 

directly as the distances and inversely as the squares of the periodic 

F D v' 2 M D 3 

times. That is, -• = - X ^ • Therefore by substitution, — — — 

/ d P 2 m d i 

P" 
X £ 2 5 tnat ^ S » the ratio of the masses is equal to the direct ratio of the 

cubes of the distances multiplied by the inverse ratio of the squares of the 
periodic times. Hence the mass oi the sun (that of the earth being one) is 
/91,430,000y / 27.3 \ 2 nHlM/wwl T , 

("238800"/ X \365i25/ ~ 315 ' 000 (ver ^ nearl y) In this calcula- 
tion, we take no account of the attraction of the earth upon the sun 
or of the moon upon the earth ; but this is so small that it would 
not affect the result materially. 

The above formula is applicable to the case of any planet that is 
attended by satellites. Thus, the masses of the earth and Saturn may 
be compared by the periodic times and distances of the moon and any 
of the satellites of Saturn. The distance of Dione is 245,846 miles, and 
its periodic time about 66 hours ; hence the cube of the ratio of the 
distance of this satellite and that of the moon multiplied by the 
square of the ratio of their periodic times, or (IHf ou) 3 X (W) 2 , will 
give the mass of Saturn, the earth being 1 By performing the work 
the result will be found to be 89 -f-, which is very nearly correct. 

The mass of the sun as compared with the earth can also be found 
by finding the force of gravity at the surface of the earth and compar- 
ing it with the force of the sun upon the earth, as determined by the 
distance and orbital velocity of the latter. 

■n D 3 M P s 

0. From the third of the above formulae it is obvious that -^ = - X -^ 

and this is evidently applicable to planets revolving around the same cen- 

M 
tral body. But in that case, the mass being the same, — becomes equal 

m 

D 3 P 2 
to 1 ; and, therefore,-^ = — 2 ; that is, the squares of the periodic 

times are in proportion to the cubes of the mean distances ; which is 
Kepler's great law. 



Question.— b. What demonstration of Kepler's third law is given ? 






CHAPTER XVI 



COMETS. 

307. Comets are bodies of a nebulous or cloudy appear- 
ance that revolve around the sun in very eccentric or 
irregular orbits, and are generally accompanied by a long 
and luminous train, called the tail. 

308. They generally consist of three parts ; the nucleus, 
or bright and apparently solid part in the centre ; the coma, 
or nebulous substance which envelops it ; and the tail, 
which extends on the side from the sun. 

a. The name comet is derived from this nebulous appearance which 
the ancients fancifully likened to hair [in the Greek, come], and hence 
called these "bodies cometce, or hairy oodles. When the luminous train 
precedes the comet, it is sometimes called the heard. 

6. The appearance of comets is not uniform, the same comet chang- 
ing very much at different times. Some comets have no nucleus, 
others, no tails ; while still others have several tails. 

c. These bodies when at a long distance from the earth and sun are 
distinguished from planets by the size and position of their orbits, and 
the direction of their motions. Uranus, it will be remembered, was 
for some time thought to be a comet, and was recognized as a plane- 
tary body only after its orbit had been proved to be almost circular, and 
nearly in the plane of the ecliptic. 

309. Comets either revolve around the sun in elliptic 
orbits, or move in curve lines called by mathematicians para- 
Mas and hyperbolas. Elliptic comets may be considered as 



Qtjestions.— 30T. What are comets? 308. Of what parts do they consist? a. 
Origin of the name b. Is the appearance of a comet uniform ? c. How distinguished 
from planets ? 809. In what kind of orbits do they revolve ? 



210 



COMETS 



belongings to the solar system; the others, only as visitants 
of it, since they come from distant regions of space, move 
around one side of the sun, and then pass swiftly away in 
paths that never return into themselves, but are constantly 
divergent. 



Fig. no. 




ORBITS OF COMETS. 



a. These paths are curve lines of peculiar properties ; they are called 
" conic sections," because they may be formed by cutting a cone in 
Various ways. Thus, if a cone be cut by a plane parallel to its base 
the curve formed will be a circle ; if both sides of the cone be cut 
obliquely by a plane, the curve will be an ellipse ; both of these curves 
are continuous lines, returning into themselves. But if the cone be 
cut by a plane parallel to either side and intersecting the base, the curve 
formed will be a parabola ; and if a plane be passed through the cone 
so as to intersect the base at an angle greater than that of the plane 
of the parabola, the resulting curve will be a hyperbola. The parabola 
and hyperbola are not continuous but divergent curves ; hence they 
do not return into themselves. The parabola is like an ellipse with 
only one focus, or an eccentricity infinitely great ; and when only a 



Question — a. Conic sections? 



COMETS. 211 

portion of it is given, it is very difficult to distinguish it from an ellipse. 
The hyperbola is more easily distinguished, because its arms or branches 
are more divergent. 

In Fig. 110 these three kinds of paths are represented ; A and P being the 
aphelion and perihelion of an elliptic orbit ;aP6, the two branches of a para- 
bolic path ; and cP d, those of a hyperbolic path. The greater divergency 
of the last will be obvious ; also, that the elliptic and parabolic curves coincide 
from 1 to 2, so as to be entirely undistinguishable. The motion indicated 
by the arrows is direct. 

310. The elements of a comet's orbit are, 1. The longitude 
of the perihelion ; 2. The longitude of the ascending node ; 
3. The inclination to the plane of the ecliptic ; 4. The eccen- 
tricity ; 5. The direction of the motion ; 6. The perihelion 
distance from the sun. 

311. The elements of more than 240 cometary orbits have 
been computed ; and of these only 19 are known to be elliptic, 
and 5 hyperbolic. The remainder are either parabolic, or 
elliptic of very great eccentricity. 

a. Besides the 19 elliptic comets mentioned, there are 37 that are 
believed to be elliptic although they have not been proved to be so ; 
and 11 others more doubtful. There are also 10 doubtful hyperbolic 
comets ; leaving, out of 242 comets whose elements have been com- 
puted, 160 with parabolic orbits, or orbits having an eccentricity too 
great to be ascertained with accuracy. 

312. The elliptic comets are divided into two classes ; 
those of short periods and those of long periods. The for- 
mer are seven in number, and have all reappeared several 
times, their identity being satisfactorily established by an 
entire correspondence of their elements. The most noted 
of these is the comet of Encke, the period of which is about 
3^ years, eighteen returns of it having been recorded. 

a. The others are De Vico's, the period of which is 5£ years ; Win- 
necke's, 5^ years , Brorsen's, 5| years; Biela's, 6f years ; D' Arrest's, 

Qxtestions. — 310. What are the elements of a comet's orbit? 311. How many have 
heen calculated ? a. Different kinds of orbits ? 312. Classes of the elliptic comets ? o. 
Which are of short period ? 



212 COMETS. 

6| years ; Faye's, 7£ years. These comets are named after the distin- 
guished astronomers who first discovered them, or determined their 
periods and predicted their returns. Several others are thought to he 
comets of short periods. 

b. These comets have comparatively small orbits, the mean distance 
of each being less than that of Jupiter, and all revolving within the 
orbit of Saturn. The inclination of the orbits is comparatively small, 
the average being about 12£°. The greatest is 31°, and the least 3°. 
They all revolve from west to east. They are not conspicuous objects, 
but have been generally visible only with the aid of a telescope. 

313. With the exception of a few comets, the periods of 
which have been computed to be about 75 years, all the 
remaining elliptic comets are thought to be of very long 
periods, some more than 100,000 years. 

a. The comet of 1744 is estimated to require nearly 123,000 years 
to complete one revolution ; that of 1844, 102,000 years ; and the great 
comet of 1680, about 9,000 years. The period of a comet can not, how- 
ever, be ascertained with precision during one appearance, since only 
a very small part of its orbit is described during the short time it 
remains visible. There is, consequently, considerable uncertainty in 
these determinations. To the great comet of 1811, the two periods of 
2,301 and 3,065 ^ears have been assigned. 

314. Of all the comets whose orbits have been ascertained, 
about one-half are direct, that is, revolve from west to east; 
the remainder are retrograde. Their inclinations are very 
diverse, some revolving within the zodiac, others at right 
angles with the ecliptic. 

a. There is a decided tendency in the periodic comets to revolve in 
orbits but little inclined to the ecliptic , while the greatest number of 
comets are found moving in or near a plane inclined 50° to the ecliptic. 
Most of the elliptic and hyperbolic comets are direct ; of the parabolic, 
retrograde. 

b. About three-fourths of all the comets have their perihelia within 
the orbit of the earth ; and nearly all the others, within the orbit of 

Questions.^-**. Size and inclination of the orbits ? 313. Comets of long period ? o. 
Examples? 814. Direction of the motion of comets? a. Tendencies of the periodic 
comets? 6. Situation of the perihelia? Aphelia? How found? 



COMETS. 213 

the nearest asteroid. Only one is situated more than 400,000,000 
miles from the sun. Some comets, on the other hand, come into close 
proximity to the sun. The great comet of 1680 approached within 
600,000 miles of it ; and that of 1843 was less than 75,000 miles. The 
aphelion distances of some of these comets are inconceivably great. 
The comet of 1811 recedes to a distance from the sun equal to 14 times 
that of Neptune, or more than, 40,000 millions of miles ; the greatest 
known (that of 1844) must be nearly 400,000 millions of miles. 

The aphelion distance can be found from the eccentricity and peri- 
helion distance. The latter in the case of the comet of 1844 is about 
80,000,000 miles ; the eccentricity, .9996 of the semi-axis. Hence 1 — 
.9996 = .0004 of the semi-axis must be the perihelion distance '; and 
80,000,000-4- .0004 = 200,000,000,000 = semi-axis. 

c. The velocity of comets as they move through their perihelia is 
amazingly great. That of 1680 was 880,000 miles an hour ; and that 
of 1843, about 1,260,000 miles an hour, or 350 miles per second. The 
latter body swept around the sun from one side to the other in about 
two hours. 

515. The number or comets is supposed to be very great. 
From the earliest period up to the present time more than 
800 have been recorded, of which nearly 300 have had their 
orbits computed, and of the latter 54 have been identified 
as returns of previous comets. 

a. Since it is only within the last 100 years that optical aid has 
been made available in searching for comets, it is supposed that the 
actual number of comets that have come within view, in both hemi- 
spheres, is not less than 4,000 or 5,000. M. Arago estimates that the 
greatest possible number in the solar system can not exceed 350,000. 

316. The size of comets, including both envelope and 
nucleus, very much exceeds that of the largest planet ; the 
nucleus is, however, comparatively small, the diameter of the 
largest measured being about 8,000 miles (that of 1845). 

a. The nucleus of the comet of 1858 (Donati's) was 5,600 miles in diam- 
eter ; that of 1811, only 428 miles. The coma of the latter was found to 

Qttestions.— c. Velocity of comets? 315. The number of comets? a. Probable 
number that have visited, or that belong to, the system? 316. Size of comets? a. 
Examples? Change of size at different times? 



214 COMETS. 

be 1,125,000 miles ; and that of Encke, 281,000 miles. The dimensions 
of comets, however, vary greatly at different parts of their orbits, con- 
tracting as they approach the sun, and expanding as they recede from 
it. Thus Encke's comet in October, 1838, was more than 250,000 miles 
in diameter ; but in December, contracted to 3,000 miles. 

317. The masses and densities of the comets must be 
inconceivably small; since, notwithstanding their great 
magnitudes, they move among the planets and their satel- 
lites without in the least, as far as it can be observed, 
affecting their motions ; although they are themselves greatly 
disturbed by the attractions of the planets. 

a. Their densities are, without doubt, many thousand times less than 
atmospheric air. Stars are seen very clearly through the nebulous 
coma and train of a comet, notwithstanding that the light has to pass 
sometimes through millions of miles of the substance. 

318. The tails of comets are often of immense length, 
and are generally of a bent or curved form, extending on the 
side from the sun and nearly in a line with the radius- 
vector of the orbit. The tail increases in length as the 
comet approaches the sun, but attains its greatest dimensions 
a short time after the perihelion passage, and then gradually 
diminishes. 

«. In respect to magnitude, the tails of comets are the most stupen- 
dous objects which the discoveries of astronomers have presented to 
our contemplation. That of the comet of 1680 was more than 100,000,- 
000 miles in length , while the comet of 1843 presented a .train 
200,000,000 miles long, which was shot forth from the head of the 
comet in the incredibly short space of twenty days. The increase of 
the tail and the decrease of the head of the comet as it approaches the 
sun, are among the most striking phenomena presented by these bodies 

b. The tails ot comets are not of uniform breadth, but diverge or 
spread out as they extend from the head. The middle of the tail 
usually presents a dark stripe which divides it longitudinally into two 
parts. This appearance is usually explained by the supposition that 

Questions.— 317. Masses and densities ? a. Why is the density thought to he small ? 
318. Position and length of tails ? a. Examples ? Change in length at different times ? 
b. Appearance of tails ? Hotv explained f 



COMETS. 215 

the tail is hollow, being a kind of conical shell of vapor ; and as we 
look through a considerable thickness of the vapor, at the edges, it 
appears brighter there than in the middle where the quantity is com- 
paratively small. 

c. The diminution of the size of comets as they approach the sun is 
probably to some extent only apparent ; since their substance must 
necessarily be vaporized as they approach the sun, and much of it so 
attenuated as to become invisible. There is no doubt also that a consid- 
erable portion is exhausted in the formation of the tail ; and that as 
the comet moves in its orbit it loses by disruption considerable portions 
which pass away into space. 

319. Observations with the polariscope have shown that 
the tails of comets shine by reflected light ; but that the 
nucleus and coma emit quite a strong radiance of their own. 

a. If the head of the comet shone by reflected light alone, its appar- 
ent brightness would be inversely proportional to the product of the 
squares of the distances from the sun and earth ; but this is contrary 
to observation. Donati's comet (that of 1858), according to this rule, 
should have been 188 times as bright when near its perihelion in Octo- 
ber as it was in June ; whereas it was actually 6,800 times as bright, its 
own light having increased in the ratio of 33 to 1. 

b. Some astronomers suppose the nucleus to be a solid, partially or 
wholly converted into vapor by the intense heat of the sun ; others, 
that it is of the same nature as the coma, only more dense. It was the 
opinion of Sir William Herschel, and is still a very generally accepted 
one, that the nucleus is surrounded with a transparent atmosphere of 
vast extent, within which the nebulous envelop floats like clouds in 
the earth's atmosphere. This nebulous matter appears to be con- 
tinually driven off" by some force emanating from the sun, and thus 
f rms the luminous train. At their perihelia comets must generally 
be subjected to a heat far more intense than would be required to melt 
the hardest substance found on the surface of the earth. Prof. Norton 
thinks that the tail is formed by two streams, in opposite magnetic or 
electric states, expelled from opposite points, or poles, of the nucleus, 
and bent back by the sun's repulsive force until they nearly meet, being 
separated by only a narrow interval, which appears as the dark stripe 
noticed in the tail. = 

Questions.^*. Change in the size of comets — how explained ? 819. Are comets self- 
luminous ? a. Why thought to be so ? b. Nature of the nucleus and the tail ? 




216 COMETS. 

REMARKABLE COMETS. 

320. Comet of 1680. — This was the comet that Newton 
subjected to the calculations by which he showed that these 

Fig. in. bodies revolve in 

one of the conic 
sections, and that 
they are retained 
in their orbits by 
the same force 
that binds the 
planets to the 
sun. It was very 
6KEAT comet op 1680. remarkable for 

its splendor, and for the extent of its train, which stretched 
over an arc of 70° in the heavens, and reached the amazing 
length of 120,000,000 miles. With the exception of the 
comet of 1843, it approached nearer to the sun than any 
other known, and moved through its perihelion with a 
velocity of 880,000 miles an hour. 

a. Its perihelion distance is .0062 (the earth's distance being 1), and 
its eccentricity, according to Encke, is .99998 Now, 91,500,000 X 
.0062 = 567,300 ; and 1 — .99998 == .00002. Hence 567,300 -s- .00002 = 
28,365,000,000, which is its semi-axis; and if we multiply this by 2, 
and subtract the perihelion distance from the product, we shall find 
the aphelion distance, which is equal to nearly 57,000 millions of miles 
The period corresponding to this orbit is 8,814 years. Some ascribe to 
this comet a much shorter period ; and others, a hyperbolic orbit. 

321. Halley's Comet. — This comet derives its name 
from Sir Edmund Halley, a celebrated English astron- 
omer, who calculated its orbit and predicted its return. It 
appeared in 1682, and Halley noticing a close resemblance 

Qttestions. — 320. How is the comet of 1680 described ? a. Its distance and period ? 
321. Halley's comet ? 



COMETS. 



217 




halley' s comet, 1835. 



in its elements to those of Fig. na. 

1531 and 1607, concluded 
that the comets of these 
years were different appear- 
ances of the same comet, and 
ventured to predict its re- 
appearance in 1758 or 1759. 
This prediction was real- 
ized hy the return of the 
comet in March, 1759; and 
it again appeared fn 1835, 
These different appearances, 
it will be observed, were about 75 years apart ; and others of 
an earlier date have also been recognized, 

a. History of the Prediction. — This celebrated prediction of 
Halley may be considered almost the first fruits of Sir Isaac Newton's 
demonstration of the laws of planetary motion as contained in his 
famous work, the Principia, published in 1687. The comet of 1682 
had been an object of interest to both Halley and Newton, and its 
"path had been calculated by Picard, Flamstead, and others. It occur- 
red to Halley that this comet might be identical with others previously 
recorded ; and fortunately the comet of 1607 had been observed by 
Kepler and Longomontanus, and that of 1531, by Apian at Ingolstadt ; 
the path in each case being quite accurately determined The coinci- 
dence which Halley noticed in these paths gave him confidence in the 
prediction which he made. He observed, however, that as the comet 
in the interval between 1607 and 1682, passed near Jupiter, its 
velocity must have been increased and its period shortened ; so that 
the next interval would be 76 years or upward, and the comet would 
return at the end of 1758 or the beginning of 1759. Subsequent 
researches gave increased force to this prediction ; for it appeared that 
comets had been seen in 1456 and 1378, whose paths seemed to have 
been nearly identical with that of the comet of 1682. 

b. The Prediction Realized. — As the time drew near, the attention 
of the scientific world was awakened to the subject ; and it was 



Questions.— a. History of the prediction? b. How was it realized ? 



218 COMETS. 

resolved to compute more exactly the time of the comet's appearance, 
by applying all the additional resources of mathematical science that 
seventy-five years had brought forth. This was a gigantic undertaking, 
since it was necessary to calculate the distance of each of the two 
planets, Jupiter and Saturn, from the comet, and the exact amount of 
their disturbance, separately, for every successive degree, and for two 
revolutions of the comet, or 150 years. Clairaut and Lalande, two 
French mathematicians, undertook the work, the latter being assisted 
in the arithmetical portion of it by Madame Lapaute ; and after six 
months spent in calculations, from morning to night, this enormous 
sum was worked out, and the day of the comet's return to its perihe- 
lion was announced. This was April 11th. . It actually passed its 
perihelion March 13th, or about 22 days previously to the predicted 
time Clairaut, however, stated in announcing his prediction that the 
comet might be accelerated or delayed by the attraction of an undis- 
covered planet beyond the orbit of Saturn, thus anticipating, in 
imagination, the discovery of Uranus which Herschel made 22 years 
afterward. Halley did not live to witness the realization of his 
prediction, having died in 1742. 

c. The Return in 1835. — The time of its perihelion passage in 
1835 was computed by several mathematicians, the mean of all the 
results being November 12th. The comet was observed to pass its 
perihelion on the 16th of that month. It continued visible in the 
southern hemisphere for several months, and then disappeared, not to 
be seen again until 1911. 

d. The mean distance of this comet is a little less than that of Uranus. 
Its perihelion distance is about 60 millions of miles; its aphelion 
distance more than 3,200 millions. Its motion is retrograde, and the 
inclination of its orbit about 18°. History shows that it has reg- 
ularly returned during a period of more than 18 centuries, its first 
recorded appearance being in 11 B.C. It seems however, to have been 
a far more conspicuous object in its ancient visitations than at its more 
recent returns. In 1066 and 1456, it was an object of immense size 
and splendor, and created wide-spread alarm. 

322. Encke's Comet is remarkable for its short period and 
frequent returns. Its period and elliptic orbit were deter- 

Questionb. — c. Return in 1835 ? d. Distance, etc. ? 322. Encke's comet f 



COMETS. 



219 




ENCKE S COMET. 



mined by Professor Encke 
at its fourth recorded ap- 
pearance in 1819. Its 
last return took place in 
1865 ; the next will occur 
in September, 1868. This 
comet has generally ap- 
peared without any lumi- 
nous train ; but in 1848, 
it had a tail about 1° 
long, turned from the 
sun, and a shorter one directed toward that luminary. In 
its latest returns it has been very faint and difficult of 
observation. 

a. Mass of Mercury. — The return of 1838 led to the establishment 
of an important fact. In August, 1835, this comet passed very near 
Mercury ; and Encke showed that, if Laplace's value of Mercury's mass 
were correct, the comet's motion would be greatly disturbed ; but as 
this was found not to be the case, it was obvious that the received 
determination of Mercury's mass needed correction. A much lower 
value has since been adopted ; but astronomers do not entirely agree 
as to this element. Encke's value is about -fa that of the earth ; but 
Leverrier's is a little more than fa. Laplace's had been about ^. 

b. The Resisting Medium. — A still more interesting discovery has 
been evolved from observations of this comet. Professor Encke found 
that at each return, the arrival of the comet at its perihelion took 
place about 2| hours earlier than the most exact calculations predicted , 
and that this constant acceleration had amounted since 1786 to about 
2 1 days. As this could not be attributed to the disturbing influence of 
any unknown body, he conceived that it could be caused only by a 
residing medium filling the interplanetary spaces ; since the effect of 
such a medium would be to diminish the centrifugal force, and thus 
bring the body nearer to the sun : so that its orbit would be con, 
tracted and its periodic time made constantly shorter. A very ethereal 
fluid would be sufficient to produce this result in the case of a body so 
light as a comet ; while it would have no appreciable effect on the 

Questions. — a. How was the mass of Mercury found ? b. Resisting medium ? 



220 



COMETS, 



planets on account of their great mass and enormous momentum. A 
similar acceleration takes place in the case of Faye's comet. 

323. Lexell's Comet. — This body is particularly noted 
for the amount of disturbance which it has suffered in pass- 
ing among the planets. Erom observations made in 1770, 
Lexell calculated its period at about 5^ years ; and it was 
a large and bright object, the diameter of its head being 
about 2|°. It has, however, never been seen since, its orbit 
having been entirely changed by planetary disturbance. 

a. Investigation showed that it really returned in 1776, but was so 
situated as to be continually hid by the sun's rays ; that in 1779, it 
passed so near Jupiter that its orbit was greatly enlarged, so that it no 
longer comes near the earth. The fact that it never appeared previous 
to 1770, is accounted for in a similar way ; its orbit having in 1767 been 
changed by the attraction of Jupiter, from one of large to one of small 
dimensions. On July 1st, 1770, the distance of this comet from the earth 
was less than 1,500,000 miles. 



Fig. 114. 




324. Comet of 1744.— 
This was the finest comet 
of the 18 th century, and 
according to some ob- 
servers, had six tails spread 
out in the form of a fan. 
Euler calculated its ellip- 
tic orbit, and assigned to 
it a period of 122,683 
years. Its motion was 
direct. 



COMET OP 1744. 



325. Biela's Comet. — 
This is one of the elliptic comets of short period ; its perihe- 
lion lying just within the orbit of the earth, and its aphelion 
a little beyond that of Jupiter. The orbit of this body 



Qtjkbtioks. — 323. Lexell's comet — why noted 
of 1744? 325. Biela's comet? 



a. How accounted for ? 324. Comet 



COMETS. 221 

nearly crosses the actual path of the earth; and in 1832, 
Olbers calculated that it would come within 20,000 miles of 
the earth, so that the latter body would be enveloped in its 
mass. The earth, however, did not reach the node until one 
month after the comet had passed it. 

a. In 1845, this comet became elongated in form and finally sepa- 
rated into two comets, which traveled together for more than three 
months ; their greatest distance apart being about 160,000 miles. The 
two parts were again seen at the next return of the comet in 1852, but 
the interval had increased to 1,250,000 miles. It has not been seen since. 

Fig. 115. 




COMET OF 1811. 

326. Comet of 1811. — This comet was very remarkable 
for its unusual magnitude and splendor. It was atten- 
tively observed by Sir William Herschel, who describes it as 
having a nucleus 428 miles in diameter, which was ruddy in 
hue, while the nebulous mass surrounding it was of a blu- 
ish-green tinge. Its tail was of peculiar form and appearance, 
extending about 25°, with a breadth of nearly 6°. 

«. The investigation of its elements by Argelander is the most com- 
plete ever made. He assigns it a period of more than 3,000 years, and 
estimates its aphelion distance at 40,121 millions of miles. 

327. Comet of 1843,-This comet was also remarkable for its 

Questions. — a. Its separation? 326. Comet of 1811 ? a. Its elements ? 327. Come c 
of 1843? 




GBEAT COMKT OF 1843. 

extraordinary size and splendor, it being visible in some parts 
of the world during the day time. It had a tail 60° long, and 
approached within a very short distance of the sun, — about 
75,000 miles from its surface. Its period is variously esti- 
mated at from 175 to 376 years. Its motion is retrograde. 

328. Donati's Comet. — This is the great comet of 1858, 
named after Donati, by whom it was first seen at Florence. 
As it approached its perihelion it attained a very great mag- 
nitude and splendor, and was particularly distinguished for 
the magnificence of its train. Its period has been estimated 
at nearly 1,900 years. 

329. Recent Comets. — About thirty comets have ap- 
peared since that of Donati, the elements of which have 
been calculated. The most remarkable were the comet of 
1861, described as one of the most magnificent on record, 
having a tail 100° long ; and that of 1862, which was very 
interesting for the peculiar phenomena which it presented 
of luminous jets, issuing in a continuous series from its 
nucleus. 



Questions. — 328. Donati' s comet? 329. Other comets. 



CHAPTER XVII. 

METEOES OR SHOOTING STARS. 

330. Meteors* or shooting stars are small luminous 
bodies that move rapidly through the atmosphere, followed 
by trains of light, and quickly vanishing from view. They 
sometimes appear in numbers so great as to seem like 
showers of stars. 

a. Star-Showers Periodical. — These star-showers are found to 
occur at certain periods. Every year, about November 14th, there is 
a larger fall than usual of meteors ; but about every 33 years, it has 
been noticed, there is a great star-shower. Those which occurred in 
November, 1866-7, had been predicted from observations of previous 
events of the kind. Thus a star-shower occurred in November, 1832-3, 
also in 1799 ; and there are eighteen recorded observations of the phe- 
nomena from 1698 to 902, all corresponding in period to that mentioned 
above. 

b. Great Star-Showers.— The shower of 1799 was awful and sub- 
lime beyond conception. It was witnessed by Humboldt and his 
companion, M. Bonpland, at Cumana, in South America, and is thus 
described by them : — " Toward the morning of the 13th of November, 
1799, we witnessed a most extraordinary scene of shooting meteors. 
Thousands of bolides and falling stars succeeded each other during four 
hours. Their direction was very regularly from north to south ; and 
from the beginning of the phenomenon there was not a space in the 
firmament, equal in extent to three diameters of the moon, which was 
not filled every instant with bolides or falling stars. All the meteors 



* From the Greek word meteora, meaning things in the air. 

Questions.— 330. What are meteors ? a. What periods have been observed in their 
occurrence ? b. What instances of great showers ? 



224 METEOBS OR SHOOTING STARS. 

left luminous traces, or phosphorescent hands hehind them, which 
lasted seven or eight seconds." The same phenomena were witnessed 
throughout nearly the whole of North and South America, and in some 
parts of Europe. The most splendid display of shooting stars on 
record was that of November 13th, 1833, and is especially interesting as 
having served to point out the periodicity in these phenomena. Over the 
northern portion of the American continent the spectacle was of the 
most imposing grandeur ; and in many parts of the country the popula- 
tion were terror-stricken at the awfulness of the scene. The ignorant 
slaves of the southern States supposed that the world was on fire, and 
filled the air with shrieks of horror and cries for mercy. The shower 
of 1866 was anticipated with great interest ; and in New York and 
other places arrangements were made to announce the occurrence, 
during the night of November 14th, by ringing the bells from the 
watch-towers. The display, however, was not witnessed in this coun- 
try, but in England was quite brilliant ; as many as 8,000 being 
counted at the Greenwich observatory. Another shower of less extent 
occurred in November, 1867. 

331. Meteoric epochs are particular times of the year 
at which large displays of shooting stars have been observed 
to occur at certain intervals. The principal of these are 
November 13th-14th, and August 6th-llfch. 

a. Three others have been established with considerable certainty ; 
namely, in January, April, and December, and still others indicated, 
that are doubtful. There are 56 meteoric days in the year; those in 
August and November being the richest. 

h. August Meteors. — Of 315 recorded meteoric displays, 63 seem 
to have occurred at this epoch. The first eleven, with one exception, 
were observed in China, between 811 A.D., and 933 A.D., and occurred a 
few days previous to August 1st. The period of this shower is exactly 
the same as the sidereal year ; and therefore it occurs about a day later 
in 71 tropical or civil years. Its maximum period is much longer than 
that of the November meteors, being estimated at 105 years. 

332. Meteors are supposed to be small bodies collected in 

Qttestions.— 331. What are the principal meteoric epochs ? a. What others ? How 
many meteoric days in a year? 6. August meteors — dates of their occurrence and 
periods ? 382. What are meteors supposed to be? 



METEORS OE SHOOTING STARS. 225 

rings or clusters, and revolving around the sun in eccentric 
orbits. They appear to resemble comets in their nature and 
origin, and, like those bodies, sometimes revolve from east 
to west. 

a. Origin of Meteors. — The immense velocity of these bodies, 
which is about equal to twice that of the earth in its orbit, or 36 miles 
a second, and the great elevation at which they become visible, the 
average being 60 miles, indicate that they are not of terrestrial, but 
cosm.ical, origin ; that is, they emanate from the interplanetary regions, 
and being brought within the sphere of the earth's attraction, precipi- 
tate themselves upon its surface. Moving with so great a velocity 
through the higher regions of the air, they become so intensely heated 
by friction that they ignite, and are either converted into vapor, or, 
when very large, explode and descend to the earth's surface as mete- 
oric stones, or aerolites* The brilliancy and color of meteors are 
variable ; some are as bright as Venus or Jupiter. About two-thirds 
are white ; the remainder yellow, orange, or green. 

h. Number of Meteors. — The average number of shooting stars 
seen in a clear, moonless night by a single observer is 8 per hour ; a 
sufficient number of observers would perceive 30 per hour, which is 
equivalent to 720 per day, seen by the naked eye at any point of the 
earth's surface, if the sun, moon, and clouds were absent. But the 
number visible over the whole earth is about 10,500 times that seen at 
a single point ; and therefore the average number daily entering the 
atmosphere, and sufficiently large to be seen by the naked eye, is more 
than 7^ millions ; while at least 50 times as many can be seen through 
the telescope ; so that about 400 millions must descend to the earth 
during the year. It becomes therefore an interesting question how 
much foreign matter may be added to the earth and its atmosphere by 
these meteoric falls. 

333. Eire balls are large meteors that make their 
appearance at a great height above the earth's surface, 
moving with immense velocity, and accompanied by luminous 



*From the Greek word aer, meaning the air, and lithos, a stone. 

Questions. — a. Their origin? Cause of their ignition? Aerolites? Color of me- 
teors? 6. Number of meteors? 333. What are fire balls ? 



226 METEORS OE SHOOTIKG STARS. 

trains. They generally explode with a loud noise, and 
sometimes descend to the earth in large masses. 

a. No deposit has been known to reach, the earth from ordinary 
shooting stars ; probably, because being very small they are dissipated 
in the air ; but scarcely a year passes without the fall of aerolites in 
some parts of the earth, either singly or in clusters. Some estimate 
the whole number that fall annually at 700 ; others, much higher. 
The most ancient fall of meteoric stones on record is that mentioned 
by Livy, which occurred on the Alban Hill, near Rome, about the year 
654 B.C. There are very many remarkable occurrences of this kind 
on record, some of the masses being of immense size, and the explo- 
sion so violent as to sound like thunder. In 1783 a fire ball of 
extraordinary magnitude was seen in Scotland, England, and France. 
It produced a rumbling sound like distant thunder, although its height 
was 50 miles when it exploded. Its diameter was estimated at about 
half a mile, and its velocity was as great as that of the earth in its orbit. 
In 1859, between 9 and 10 o'clock A.M., a meteor of immense size was 
seen in the eastern part of the United States. Its apparent diameter 
was nearly equal to that of the sun ; and it had a train several degrees 
in length, plainly visible in the sunshine. Its disappearance on the 
coast of the Atlantic was followed by several terrific explosions. Some 
of these meteors have been supposed to pass the earth, moving away 
into space ; others to revolve in an orbit around it, becoming small 
satellites. A French astronomer assigns to one of the latter a period of 
revolution of 3 hours and 20 minutes, and a distance from the earth of 
5,000 miles. 

b. Composition and Size of Aerolites. — The materials composing 
these bodies are always nearly the same, consisting largely of iron, 
and in no case of any other elementary substances than are found on 
the earth. Some have been discovered of immense size ; one, a mass 
of iron and nickel, found in Siberia, weighs 1,680 lbs. At Buenos Ayres 
there is a mass partly buried in the ground 7£ feet in length, and sup- 
posed to weigh about sixteen tons. A similar block, weighing about 
six tons, was discovered a few years ago in Brazil. Many others exist. 
All these are doubtless of cosmical origin, having been very small 

Questions.— a. Frequency of the fall of aerolites? Earliest recorded instance? 
Remarkable instances ? Do they all reach the earth ? 6. Composition of aerolites ? 
Their size ? Additions to the earth, Venus, and Mercury from this cause ? Effect on 
Mercury's period? 



METEORS OR SHOOTING STARS. 227 

planets revolving around the sun, but brought within the earth's 
attraction ; and there is no doubt that, before the solar system had 
reached its present condition, the additions made to the matter of 
the earth in this way were quite considerable. This is supposed 
still to be the case with Venus and Mercury, moving as they are 
through the thicker portions of the great ring which we call the 
zodiacal light. Now, as Mercury's orbit is very eccentric, it receives at 
its aphelion a large number of these meteors whose periods are longer 
than its own ; and this would have the effect to diminish its mean 
motion and lengthen its period. Such an effect has actually been 
discovered. 

c. Meteoric Dust, etc. — There are on record many instances of 
showers of dark -colored dust, which have fallen from the higher 
regions of the atmosphere, and which seem from the composition of 
the dust to be of meteoric origin. These falls are often preceded or 
attended by a flashing of light as well as by a loud noise, sometimes 
resembling thunder. In March, 1813, a shower of red dust fell in 
Tuscany, discoloring the snow which then lay on the ground ; and at 
the same time, a few miles distant, there occurred a shower of aero- 
lites, lasting about two hours, and accompanied by a noise as of the 
dashing of waves. The phenomena of black and red rain and snow are 
attributed to a similar cause. Since, as has been shown, several mil- 
lions of meteors pass into the atmosphere during the year, there is no 
doubt that large quantities of dust, too fine to be visible, descend to 
the earth's surface. Some of this dust has been detected upon the 
tops of mountains in soil which had never been previously disturbed 
by man. Partial obscurations of the sun's light, occasioning what are 
recorded as dark days, and the passage of large black masses across 
the sun's disc, too rapid to be spots, are probably meteoric phenomena. 

334. The November meteors are supposed to revolve 
around the sun in an orbit of considerable eccentricity, 
inclined to the plane of the ecliptic in an angle of 173°, 
and extending at its aphelion somewhat beyond the orbit of 
Uranus, its perihejion being very nearly at that of the earth. 
They move in a ring of unequal width and density, the 

Questions.— c. Showers of dust? Black and red rain ? 334. Orbit of the November 
meteors? Why visible only every 33 years? 



228 METEORS OR SHOOTING STARS. 

thickest part crossing the earth's orbit every 33 years, and 
requiring nearly two years to complete the passage. 

a. The elements of this orbit correspond almost precisely with 
those of the comet which made its appearance in January, 1866 ; so 
that it seems probable that the comet is a very large meteor of the 
November stream. The elements of the orbit of the August meteors 
have been found, in a similar manner, to coincide with those of the 
third comet of 1862 ; showing that the comet and these meteors belong 
to the same ring. This seems also to be true of the first comet of 
1861 and the April meteors. 

6. The point from which the November meteors seem to radiate is 
in the constellation Leo ; because, as the earth at that time of the year 
is moving toward that point, they appear to rush from it. Their veloc- 
ity appears to be double that of the earth, although only equal to it ; 
because they move in an opposite direction and almost in the same 
plane. When the earth plunges into the meteoric stream a great star- 
shower occurs. 

c. Physical Origin. — Meteors are supposed by some to be small 
fragments of nebulous matter detached in vast numbers from the 
larger masses which are seen in the regions of the stars, or from 
that of which the solar system was originally formed, their origin 
being precisely the same as that of the comets, which indeed may 
be considered as, in reality, only meteors of vast size. It is also 
probable that, like Biela's comet, others have been divided and 
subdivided so as finally to be separated into small fragments moving 
in the orbit of the original comet, and thus constituting a meteoric 
ring or stream. 

d. The following general conclusions with regard to meteors in the 
solar system have been suggested : 1. Biela's comet in 1845 passed very 
near, if not through, the November stream, and was probably divided 
in this way ; 2. The rings of Saturn are dense meteoric streams, the 
principal or permanent division being due to the disturbing influence 
of the satellites ; 3. The asteroids are a stream or ring of meteors, 
the largest being the minor planets which have been discovered ; 4. 
The meteoric masses encountered by Encke's % comet may account for 
the shortening of the period of the latter without the hypothesis of a 
resisting medium. 

(^testions. — a. Resemblance to comets? b. Radiant point of November meteors? 
e. Physical origin of the meteors? d. Generalizations with regard to meteors in the 

solar system? 



CHAPTER XVIII. 

THE STARS. 

335. The stars are luminous bodies like the sun, but 
situated at so vast a distance from the earth that they seem 
like brilliant points, and always in nearly the same positions 
with respect to each other. 

a. The scintillation or twinkling of the stars is due to the 
inequalities in density, moisture, etc., of the different strata of the 
atmosphere through which the rays of light pass. In tropical regions, 
where the atmospheric strata are more homogeneous, this scintillation 
is rarely observed ; so that, as remarked by Humboldt, " the celestial 
vault of these countries has a peculiarly calm and soft character." 

b. Parallax of the Stars. — The usual method of finding the par- 
allax of a body by viewing it at different parts of the earth's surface 
is entirely useless in the case of the stars, as the displacement thus occa- 
sioned in the positions of any of them is utterly inappreciable ; the 
radius of the earth at a distance so immense being practically but a 
mathematical point. If, however, we view the same star at intervals 
of six months, our stations of observation will be about 180 millions 
of miles apart ; and the amount of displacement thus occasioned, when 
reduced to the centre of the orbit, is the stellar parallax, called some- 
times the annual parallax. 

336. The annual parallax is the change which would 
take place in the position of a star if it could be viewed 
from the centre of the orbit, instead of the orbit itself. 

a. In other words, it is the angle subtended by the semi-axis of the 

Questions.— 335. What are the stars? a. Cause of the scintillation ? b. Parallax of 
the stars, how found? 386. How is annual parallax defined ? a. Greatest parallax ? 



230 THE STAES. 

earth's orbit at the distance of the star. The greatest parallax yet 
discovered in the case of any star is somewhat less than 1" (0.9187"), 
so that the earth's orbit itself is but little more than a mere point at 
the nearest star. To determine this small parallax exactly is prob- 
ably the most difficult problem in practical astronomy. 

b. Distance Calculated.— The sine of 0.9187" is about .000004464, 
which is the ratio of the semi-axis of the earth's orbit to the distance 
of the star. Hence the distance of the star must be 224,000 times the 
semi-axis of the earth's orbit, or 91£ millions of miles ; and 91,500,000 
X 224,000 = 20,496,000,000,000 miles, or nearly 20£ trillions of miles. 
Light, moving with a velocity of 184,000 miles a second, requires more 
than 3* years to pass across this enormous interval, — an interval more 
than 7,000 times the distance of Neptune from the sun. However 
large the stars may be, therefore, their attraction upon the solar system 
must be altogether too feeble to disturb the motions of its component 
bodies in the least. The parallax of twelve stars has been determined 
with considerable precision, the smallest being 0.046", or about one- 
twentieth that mentioned above ; this star must therefore be about 
410 trillions of miles from us, — a distance which light would not traverse 
in less than 70.3 years. 

337. Magnitudes. — The stars are divided into classes 
according to their apparent brightness, the brightest being 
distinguished as stars of the first magnitude, the next of the 
second, and so on. Stars of the first six magnitudes are visi- 
ble to the naked eye ; but the telescope reveals the existence 
of others so feeble in light as to be classed as of the seven- 
teenth magnitude. 

a. This classification is based exclusively on appearance, and indi- 
cates nothing as to the real magnitudes of the bodies in question. Sir 
John Herschel gives the following comparative estimate of the amount 
of light emitted by stars of the first six magnitudes : 

3d magnitude = 12 
2d " = 25 

1st " = 100 

Questions.— &. Distance of the stars, how calculated ? Of how many stars has 
the parallax heen found ? The least ? 337. Magnitudes of the stars ? How many f 
a. What does magnitude indicate ? Comparative brilliancy of each ? 



6th 


magnitude 


= 


1 


5th 


u 


= 


2 


4th 


tt 


= 


6 



THE STARS. 231 

This is not uniformly the relative brightness of stars thus denominated ; 
Sirius, the brightest star in the heavens, being 324 times as brilliant as 
an average star of the 6th magnitude. 

338. The whole number of stars visible to the naked 
eye in the northern hemisphere is about 2,400; in both 
hemispheres, more than 4,500. 

a. These are distributed by Argelander according to their magni- 
tudes as follows : 1st magnitude, 9 ; 2d, 34 ; 3rd, 96 ; 4th, 214 ; 5th, 
550 ; 6th, 1439 ; total in northern hemisphere, 2,342. If the southern 
hemisphere is equally rich in stars, the whole number must be 4,684 ; 
some estimate it at 6,000 or 7,000. The stars are probably less bright 
in proportion as their distance is greater; and hence the number 
increases as we descend to the lower magnitudes. Argelander's 
estimate for the 9th magnitude is 142,000. Viewed through the tele- 
scope, the stars can be counted by millions. 

THE CONSTELLATIONS. 

339. To facilitate the naming and location of the stars, 
the heavens are divided into particular spaces, represented 
on the globe or map as occupied by the figures of animals 
or other objects. These spaces and the groups of stars 
which they contain are called constellations, or asterisms. 

a. Thus there are the constellations Aries, the Ram ; Leo, the 
Lion ; Gemini, the Twins, etc. The general position of a star, accord- 
ing to this system, is defined by stating in what part of the figure it is 
situated ; as, the eye of the Bull, the heart of the Lion, etc. Its exact 
position is, of course, only to be defined by its right ascension and 
declination, or longitude and latitude. This system of grouping the 
stars into constellations is supposed to be very ancient. Ptolemy 
counted only forty-eight constellations ; but, since his time, the num- 
ber has been augmented to 109. 

340. The stars belonging to each constellation are distin- 
guished by particular names ; as Sirius, Regulus, Arcturus, 
etc., and by letters or numerals. 

Qukstionb.— 338. What number of visible stars ? a. How distributed ? 339. Con- 
stellations? a. How used ? Number enumerated by Ptolemy ? By modern astronomers ? 
340. Mode of designating the stars ? 



232 



THE STABS, 



a. Only the most conspicuous stars have particular names ; the most 
usual mode of designation being the use of the letters of the Greek 
alphabet, alpha (a) being given to the brightest star, beta (0) to the 
next, and so on. When the twenty-four letters of this alphabet are 
exhausted, the Roman letters are used, and subsequently the Arabic 
numerals, the latter being applied according to the positions of the 
stars in the constellation, the most eastern being designated 1, which 
is thus the first star to cross the meridian. 

b. The Greek Alphabet. — The following are the letters of the 
Greek alphabet, with their names. It will be convenient for the student 
to become familiar with them, as they are very frequently employed. 



a Alpha 


V Eta 


v Nu 


r Tau 


Beta 


Theta 


1 Xi 


v Upsilon 


y Gamma 


i Iota 


o Omicron 


<j> Phi 


6 Delta 


k Kappa 


7T Pi 


X Chi 


e Epsilon 


X Lambda 


p Rho 


V> Psi 


? Zeta 


H Mu 


a Sigma 


w Omega 



341. The constellations are distinguished as Northern, 
Zodiacal, and Southern, according to their positions in the 
heavens with respect to the ecliptic. The zodiacal constel- 
lations have the same names as the signs, hut are situated 
about 28° to the east of them, so that Aries, although the 
first sign of the ecliptic, is the second constellation of the 
zodiac (Art. 105, b). 

342. The whole number of constellations is 109; hut 
many of them are not generally acknowledged or much 
used by astronomers at the present time. 

a. The following catalogue contains the names of the principal con- 
stellations, with their right ascension and declination, the number of 
stars of the first five magnitudes contained in each, and the name of 
the astronomer by whom they were first enumerated or invented : 

Note. — The right ascension and declination of the central points of the 
constellations are given. 



Questions.— a. Use of letters? Of numerals? Letters of the Greek alphabet? 
841. How are the constellations divided ? 342. What is the whole number of constel- 
lations ? Are all acknowledged and used ? a. Which are the principal Northern 
constellations? Zodiacal constellations? Name the Southern counstellations. 



THE STARS, 



233 



THE NORTHERN CONSTELLATIONS. 







1 


By whom 


£ fc 






© 


Name. 


Meaning. 


enumerated 


< c 


R.A. 


Deo. 


£i 




OR INVENTED. 


£fc 






1 


Andromeda, 


The Chained Princess, 


Ptolemy, 150 


18 


15° 


35° 


2 


Aquila, 


The Eagle, 


Ptolemy. 


33 


2921° 


10° 


3 


AURIGA, 


The Charioteer, 


Ptolemy. 


35 


90* 


42° 


4 


Bootes, 


The Bear Driver, 


Ptolemy. 


35 


219° 


80° 


5 


CaMELOPARDALUS, 


The Giraffe, 


Hevelius, 1690. 


36 


86° 


€8° 


6 


Canes Venatici, 


The Hunting Dogs, 


Hevelius, 16i)0. 


15 


195° 


40° 


7 


Cassiopeia, 


The Queen in her Chair, 


Ptolemy. 


46 


lf|° 

825° 


60° 


8 


Cepheus, 


The King, 


Ptolemy. 


44 


65° 


9 


Clypeus Sobieskii, 


SobieskVs Shield, 


Hevelius, 1690. 


4 


2721° 


15° S 


10 


Coma Berenices, 


Berenice's Hair, 


Tycho Brahe, 
1603. 


20 


190° 


25° 


11 


Corona Bobealis, 


The Northern Crown, 


Ptolemy. 


19 


235* 


30° 


n 


Cygnus, 


The Swan, 


Ptolemy. 


67 


3(5° 


42° 


13 


Delphinus, 


The Dolphin, 


Ptolemy. 


10 


310° 


15° 


14 


Draco, 


The Dragon, 


Ptolemy. 


80 


260° 


66* 


15 


Equuleus, 


The Little Horse, or 
Horses Head. 


Ptolemy. 


5 


315° 


6* 


16 


Hercules, 


Hercules, 


Ptolemy. 


€5 


251° 


27° 


17 


Lacekta, 


The Lizard, 


Hevelius, 1690. 


13 


8C5° 


44° 


IS 


Leo Minor, 


The Lesser Lion, 


Hevelius, 1690. 


15 


151° 


36° 


19 


Lynx, 


The Lynx, 


Hevelius, 1690. 


28 


120° 


50* 


20 


Lyra, 


The Harp, 


Ptolemy. 


18 


280° 


85° 


21 


Pegasus, 


The Winged Horse, 


Ptolemy. 


43 


836° 


15° 


22 


Perseus et Caput Me- 
dus^e, 


Perseus & Medusa's 
Head, 


Ptolemy. 


40 


52|° 


47° 


23 


Sagitta, 


The Arrow, 


Ptolemy. 


5 


295° 


18* 


24 


Serpens, 


The Serpent, 


Ptolemy. 


23 


285° 


10° 


25 


Taurus Poniatowskh, 


PoniatowskVs Bull, 


Poczobut, 1777 


6 


267i° 


5° 


26 


Triangulum, 


The Triangle, 


Ptolemy. 


5 


80° 


82° 


27 


Ursa Major, 


The Great Bear, 


Ptolemy. 


53 


160° 


58* 


28 


Ursa Minor, 


The Lesser Bear, 


Ptolemy. 


23 


225° 


78° 


29 


VULPECULA ET AN8ER, 


The Fox and the Goose. 


Hevelius, 1690. 


23 


800° 


25° 



THE ZODIACAL CONSTELLATIONS. 



Name. 



Meaning. 



By whom 
enumerated. 



c a 



K.A. 



Dec. 



1 


Aries, 


The Ram, 


Ptolemy. 


17 


37i° 


18° N 


2 


Taurus, 


The Bull, 


Ptolemy. 


58 


60° 


18°" 


3 


Gemini, 


The Twins, 


Ptolemy. 


28 


105° 


25° " 


4 


Cancer, 


The Crab, 


Ptolemy. 


15 


130° 


20°" 


5 


Leo, 


The Lion, 


Ptolemy. 


47 


155° 


15°" 


6 


Virgo, 


The Virgin, 


Ptolemy. 


89 


200° 


3°" 


. i 


Libra, 


The Balance, 


Ptolemy. 


23 


225° 


15° S 


8 


Scorpio, 


The Scorpion, 


Ptolemy. 


84 


244° 


26°" 


y 


Sagittarius, 


The Archer, 


Ptolemy. 


38 


285° 


82° ■ 


10 


Capricornus, 


The Goat, 


Ptolemy. 


22 


315° 


20° " 


n 


Aquarius, 


The Water- Carrier, 


Ptolemy. 


25 


880° 


9°» 


12 


Pisces, 


The Fishes, 


Ptolemy. 


18 


5° 


10° N 



234 



THE STARS. 



THE SOUTHERN CONSTELLATIONS. 









By whom 


. <o 






© 


Name. 


Meaning. 


enumerated 


O M 
/5 < 


R.A. 


Deo. 






OR INVENTED. 


CD 






1 


Apis or Musca, 


The Bee or Fly, 


Bayer, 1604. 


7 


186* 


68° 


2 


Aba, 


The Altar, 


Ptolemy. 


15 


256' 


54° 


3 


A ego, 


The Ship Argo, 


Ptolemy. 


133 


115° 


50° 


4 


Canis Major, 


The Great Dog, 


Ptolemy. 


27 


101° 


24° 


5 


Canis Minor, 


The Lesser Dog, 


Ptolemy. 


6 


111° 


5°N 


6 


Centaur us, 


The Centaur, 


Ptolemy. 


54 


195° 


48° 


7 


Cktus, 


The Whale, 


Ptolemy. 


32 


80° 


12° 


8 


COLUMBA NOAOHI, 


Noah's Dove, 


Eoyer, 1679. 


15 


81° 


85° 


9 


Corona Austbalis, 


The Southern Crown, 


Ptolemy. 


7 


-77-r 

1«5° 


40° 


10 


Corvus, 


The Crow, 


Ptolemy. 


8 


18* 


11 


Crater, 


The Cup, 


Ptolemy. 


9 


170° 


15° 


12 


Critx, 


The Cross, 


Koyer, 1679. 


10 


184° 


60° 


13 


Dorado, 


The Stcord-Fish, 


Bayer, 1604. 


17 


70° 


62° 


14 


Ekidanub, 


The River Po, 


Ptolemy. 


64 


85° 


80° 


15 


Gnus, 


The Crane, 


Bayer, 1604. 


11 


335° 


47* 


16 


Hydra, 


The Snake, 


Ptolemy, 


49 


150° 


10° 


17 


H yd bus, 


The Water- Snake, 


Bayer, 1604. 


25 


40° 


70' 


18 


Indus, 


The Indian, 


Bayer, 1604. 


15 


315° 


55* 


19 


Lepus, 


The //are, 


Ptolemy. 


18 


81° 


20- 


20 


Lupus, 


The WW/ 


Ptolemy. 


84 


231° 


45° 


21 


Monoceros, 


The Unicorn, 


Hevelius, 1690. 


12 


105° 


2° 


22 


Ophiuchus or Serpen- 

TARIUS, 


The Serpent Carrier, 


Ptolemy. 


40 


255° 


0* 


23 


Orion, 


The Huntsman, 


Ptolemy. 


37 


S2i° 


0° 


24 


Pavo, 


The Peacock, 


Bayer, 1690. 


27 


290° 


C8° 


25 


Phojnix, 


The Pho&nvx, 


Bayer, 1690. 


82 


15° 


60- 


26 


Piscis Australis, 


The Southern Fish, 


Ptolemy, 


16 


125° 


32* 


27 


Toucan, 


The .dmertcaw Goose, 


Baver, 1690. 


21 


)56' 


66° 


28 


Triangulum Australe, 


The Southern Triangle, 


Bayer, 1690. 


11 


235° 


65° 



b. History of the Constellations. — The following is a hrief 
account of the origin of the constellations : 

THE NORTHERN CONSTELLATIONS. 

Andromeda, daughter of Cepheus, king of Ethiopia, who, to save 
his kingdom, caused her to be bound to a rock so that she might be 
devoured by a sea monster ; but she was rescued by Perseus, who 
turned the monster into stone by presenting to it the head of Medusa, 
the Gorgon Queen, whom he had conquered and slain. 

Aquila, according to the ancient fable, was king of one of the 
Cyclades, but was changed into an eagle and placed among the stars. 
Tycho Brahe added to this constellation Antinous, a youth of Asia 
Minor, greatly celebrated for his beauty, who lived in the reign of the 
Emperor Adrian. 



Question.— 6. What is the history of each ? 



THE STARS. 235 

Auriga, represented as a man kneeling, and holding a bridle in Lis 
right hand, and a goat with her kids in his left. The accounts given 
of this constellation are various and inconsistent. Its origin is un- 
known. 

Bootes, represented as grasping a club in one hand, while he holds 
the two hunting dogs by a cord, in the other. He seems to be driving 
the two bears round the pole. The origin of this constellation is lost 
in antiquity. 

Canes Venatici, called Asterion and Chara, inserted by Hevelius, 
in 1690. They are held in a leash by Bootes. 

Cassiopeia, the wife of Cepheus and mother of Andromeda. 

Cepheus, king of Ethiopia, supposed to have gone with the Argo- 
nauts in search of the golden fleece. 

Clypeus or Scutum Sobieskii, named in honor of John Sobieski, 
King of Poland, by Hevelius, who flourished during his reign. 

Coma Berenices. — Berenice was the Queen of Ptolemy Euergetes, 
one of the kings of Egypt ; and while he was engaged in war, she 
made a vow to dedicate her beautiful hair to Venus if he returned in 
safety, — a vow which she fulfilled. 

Corona Borealis, a beautiful crown said to have been given by the 
god Bacchus to Ariadne, a Cretan princess. 

Cygnus, supposed by some to represent the famous musician 
Orpheus, who, according to the fable, was changed into a swan, and 
placed near his lyre in the heavens. 

Delphinus, the dolphin who is said, in the fable, to have persuaded 
Amphitrite to become the wife of Neptune, though she had made a 
vow of perpetual celibacy. 

Draco, supposed to be the dragon which guarded the golden apples 
in the garden of the Hesperides, near Mount Atlas, and was slain by 
Hercules. 

Equuleus is the head of a horse, supposed to have been the brother 
of Pegasus, and given to Castor by Mercury. 

Hercules, the famous Grecian hero, celebrated for his many won- 
derful exploits. 

Lyra, the harp given to Orpheus by Apollo, upon which he played 
with such skill, that even the rivers, it is fabled, ceased to flow in order 
to listen to his strains. 

Pegasus, the winged horse, which, according to the Greek fable, 
sprung from the blood of Medusa, after Perseus had cut off her head. 
Bellerophon, attempting to fly to heaven upon his back, was dashed to 



236 THE STABS. 

the earth ; and the horse continuing his flight was finally placed by 
Jupiter among the constellations* 

Perseus, son of Jupiter and Danae, was provided with celestial arms, 
and made war upon the three Gorgons, who had the power to turn 
every one to stone on whom they looked. Medusa was the most 
celebrated for her beauty ; but her hair was turned to serpents by 
Minerva, the sanctity of whose temple she had violated. (See An- 
dromeda.) 

Sagitta, the arrow of Hercules with which he killed . the vulture 
that preyed on Prometheus, who was tied to a rock on Mount Cauca- 
sus by command of Jupiter. 

Serpens and Serpentarius, or Ophiuchus. — The latter is supposed 
to be iEsculapius, a famous Greek physician. He holds the serpent in 
his hand as an emblem of his art, the cure of a serpent's bite being a 
test of medical skill. 

Taurus Poniatowskii, a small constellation, some of the stars of 
which are arranged like a V, fancied to resemble a bull's head, and 
named as above after Count Poniatowski, who saved the life of Charles 
XII. King of Sweden, at the battle of Pultowa, and afterward at the 
battle of Rugen. 

Triangulum. — This constellation represents the triangular delta of 
the Nile. 

Ursa Major, suposed to represent Calisto, daughter of a king of 
Arcadia, and changed into a bear in consequence of the jealousy of Juno. 
Ursa Minor is supposed to have been her son Areas, changed with her. 
These constellations are sometimes called Triones ; also, the Greater 
and Lesser Wains. 

THE ZODIACAL CONSTELLATIONS. 

These are supposed to have been invented by the Egyptians or 
Chaldeans to symbolize the changes of the months and seasons. The 
following is their origin according to the Greeks : 

Aries is the ram that bore the golden fleece, for which the Argonauts 
undertook their expedition. 

Taurus is supposed to be the bull whose form Jupiter assumed in 
order to carry off Europa, a beautiful princess of Phoenicia. She was 
borne across the sea to Europe, and gave name to that country. This 
constellation contains five stars arranged in the form of a V, and 
called the Hyades. It also contains the Pleiades, or seven stars, as 



THE STARS. 237 

the number is declared by some of the ancients, although only six are 
now visible. . 

Gemini, the twin brothers Castor and Pollux, sons of Jupiter and 
Leda, a Spartan queen. They were celebrated for their valor and 
heroic deeds, and were afterward worshiped as deities. 

Cancer, the sea-crab, sent by Juno to annoy Hercules. This con- 
stellation more probably symbolizes the backward movement of the 
sun when at the northern solstice. 

Leo, the famous Nemean lion, slain by Hercules ; or a symbol of 
the intense heat of the season when this asterism is on the meridian. 

Virgo, the Virgin Astrsea, goddess of justice, who lived on earth 
during the golden age, but returned to heaven and was placed among 
the stars. A symbol, probably, of the time of harvest, as she holds an 
ear of corn (spica virginis) in her hand. 

Libra, the scales which Virgo, the goddess of justice, used as an 
emblem of her office. Most probably it was an emblem of the bal- 
ance or equality of the days and nights. 

Scorpio, a very ancient constellation, supposed to typify the deadly 
influences of the season when the sun is in this part of the ecliptic. 
According to Ovid, it is the scorpion which stung Orion and caused his 
death. 

Sagittarius, emblem of the hunters' season, inscribed on the Egyp- 
tian Zodiac. According to the Greeks, it represents Chiron, the 
famous Centaur, who changed himself partly into a horse. 

Capricornus, emblem of the sun's climbing (as a goat) from the 
winter solstice. In the Greek fables, it is the goat into which Bacchus 
changed himself to escape the giant monster Typhon. 

Aquarius, emblem of the wet season. The Greeks took it for 
Ganymede, the cup-bearer of Jupiter. 

Pisces, emblem of the fishing season. The Greeks represent them 
to be the fishes into which Venus and Cupid changed themselves to 
escape the giant Typhon. 

THE SOUTHERN CONSTELLATIONS. 

Ara, the altar on which, according to the ancient mythology, the 
gods swore before their celebrated contest with the giants. 

Argo, the ship in which the Argonauts sailed in quest of the golden 
fleece. 

Oanis Major and Canis Minor, supposed to be Orion's hounds. 



238 THE STARS. 

Centaurus, one of the Centaurs, a fabulous race, half men and half 
horses ; most probably a tribe of men who invented, or were skilled 
in, the art of breaking in horses. 

Cetus, the sea monster from which Andromeda was rescued by 
Perseus. 

Corvus, the crow sent by Apollo to watch the conduct of his mis- 
tress Coronis, and rewarded by being placed in the heavens. 

Crater. — The origin of this constellation appears to be unknown. 

Crux, formed by Royer as a Christian emblem. It contains four 
stars that form a cross, two of them pointing directly to the south pple. 

Bridanus, the river Po, fabled to have received Phaeton, who, having 
undertaken to guide the chariot of the sun, was struck by Jupiter with 
a thunderbolt, to prevent the general conflagration of the world from 
the ignorance of the rash youth. 

Hydra, a monstrous serpent killed by Hercules. It is supposed by 
some to symbolize the moon's course. 

Lepus, placed near Orion, as being one of the animals hunted by 
him. 

Lupus, a king of Arcadia, Lycaon, changed into a wolf on account 
of his cruelties. 

Ophiuchus. — See Serpens. 

Orion, according to the Greeks, a famous hunter, who, as a punish- 
ment for his profane boasting, was bitten by the scorpion and killed. 
This constellation is mentioned in the book of Job, and is therefore of 
very great antiquity. Some think that it represents Nimrod, " the 
mighty hunter," mentioned in Genesis. 

Piscis Australis, supposed by the Greeks to be Venus, transformed 
into a fish to escape the giant Typhon. 

c. Of the 48 constellations enumerated by Ptolemy in his great 
work, the Almagest, all except three are described in a poem styled 
Phenomena, written in Greek by Aratus, a Cilician poet, 270 B.C., 
and still extant. This poem is, however, only a paraphrase of a 
celebrated work written about 370 B.C. by Eudoxus, a contemporary 
of Plato, and containing an account of all the constellations used in 
his time. 

d. The following synopsis shows the relative positions as to right 

Questions. — d. Names of the constellations in the circle of perpetual apparition, from 
west to east? Between 50°and 25° of north declination? Between 25° and 0° ? Be 
ween 0-° and 25° S ? Between 25° and 50° S ? 



THE STAKS. 



239 



ascension and declination of the constellations visible in this latitude. 
If studied in this order they will be found without difficulty on the 
globe or in the heavens. 
Note.— Each line in this table represents about 30° of right ascension. 

TABLE SHOWING THE POSITIONS OF THE CONSTELLA- 
TIONS IN THE HEAVENS. 



North Declination. 



South Declination. 



90°— 50° 


60°— 25° 


25°— 0° 


Zodiac. 


0°— 25° 


25°— 50° 


Cassiopeia 


Andromeda 




Pisces 


Cetus 






Triangulum 




Aries 




Phoenix 


Camelopard. 


Perseus 




Taurus ■] 


Lepus j 
Orion ( 


Eridanus 
Columba 




Auriga 


Canis Minor 


Gemini -J 


Canis Major 


Argo 




Lynx 




Cancer 






Ursa Major 


Leo Minor 




Leo -J 


Hydra 

Crater 






Canes Ven. 


Coma Ber. 


Virgo 


Corvus 


Centaurus 


Ursa Minor -J 


Bootes 
Corona Bor. 


Serpens 


Libra 




Lupus 


Draco 


Hercules 


Taurus Fon. 


Scorpio 


Ophinchus 






Lyra \ 


Sagitta 
Aquila 


Sagittarius 


Clyp. Sobiesk. 


Corona Aus. 


Cepbeus •< 


Lacerta j 
Cygnus 1 


Delphinus 
Bqutileus 


Capric(vrn us 










Pegasus 


Aquarius 




Grus 



c. Each column of this table contains the constellations as they 
are arranged from west to east ; and each line read from left to right, 
gives the constellations, from north to south, that are on or near the 
meridian at the same time. By knowing the time that each zodiacal 
constellation comes to the meridian, remembering that these constel- 
lations are about 30° east of the signs, and that those are on the 
meridian at midnight which are opposite to the sun's place at noon, 
the student with a little consideration will be able to find the position of 
the constellations at any hour and on any evening during the year. 
The position at any time of the evening can easily be deduced from 
that at midnight by reckoning for each hour 15°, toward the east if 
the time is earlier, and toward the west, if later. 

Question. — Use of the table? 






240 



THE STARS, 



343. Star Names. — Only a very few of the stars are dis- 
tinguished by particular names, the usual mode of designation 
being by means of letters or numbers. 

The following is a list of the most noted or conspicuous of the stars 
with their special names, literal designations, magnitudes, and situations : 

Note.^Iu the literal designations, the letter is followed by the Latin 
name of the constellation, in the possessive case; thus, a Centaurl means 
the brightest star of Centaurus ; /3 Tauri, the second star of Taurus ; y Cas- 
siopeia, the third star of Cassiopeia, etc. The stars are arranged in this 
list according to their magnitudes. 

LIST OF PRINCIPAL STARS. 



Name. 


Literal Designation. 


Situation. 


E 

100° 


Dec. 


Struts 


a Canis Majoris 


Nose of the Great Dog 1 


i«r 8 


Canopus 


a Argus 


The Ship Argo 1 


95° 


52>° s 


ARCTURUS 


a Bootis 


Knee of Bootes 1 


212" 


20° N 


Betelgeuse 


a. Orionia 


Shoulder of Orion 1 


87" 


7i°N 


RlGEL 


j3 Orionis 


Foot of Orion 1 


77° 


8J- S 


CAPELLA 


a Auriga 


Goat of Auriga 1 


77° 


46° N 


Vega 


a Lyra* 


One of the strings of the Harp 1 


278° 


39° N 


Prooton 


a Canis Minoria 


The Little Dog 1 


113° 


5i*N 


ACHERNAR 


a Eridani 


The River Po 1 


23° 


58° S 


Aldebaran 


a Tauri 


Eye of the Bull 1 


67= 


16i°N 


Antares 


o Saorpionia 


Heart of the Scoupion 1 


1 245° 


26° S 


Altair 


a. Aquilce 
a Virginia 


Neck of the Eagle 1 


800* 


8„i°N 


8 PIC A 


Sheaf of Virgo 1 
Southern Fish 1 


200° 


10|° 8 


FOMALHATXT 


a Piscis Aust. 


343° 


30i° S 


Eegulus 


a Leonis 


Heart of the Lion 1 


150" 


45° N 


Deneb 


a Cygni 


Tail of the Swan I 


309° 


Alpheratz 


a Andromeda 


Head of Andromeda 1 


- 10 

• 2 


28|° N 


DUBHE 


a Ursce Majoria 


Great Bear 1 


\ 164° 


62i°N 


Castor 
Pollux 


a Geminorum \ 

/3 Geminorum j 


Heads of Gemini 2 


\ 112° 
114° 


32° N 
2SJ° N 


Pole-Star 


a Ursce Minoris 


Tail of Little Bear 2 


18J' 


88|°N 
8° 8 


Alphard 


a Hydrce 


Heart of Hydra 2 


140° 


Eas Alhagus 


a Ophiuehi 


Head of Serpent-bearer 'i 


262° 


12i°N 


Markab 


a Pegasi 


Wing of Pegasus 2 


345° 


14|°N 


So HEAT 


Pegasi 


Thigh of Pegasus 2 


345° 


27£° N 


Algenib 


y Pegasi 


Wing of Pegasus 2 


2° 


14|° N 


Algol 


|3 Persei 


Head of Medusa 2 


\ 45° 


40i° N 


Denebola 


3 Leonis 


Tail of the Lion 2 


\ 176° 


15° N 


Alphecca 


a Coronce Bor. 


Northern Crown 2 


I 282° 


27° N 


Benetnasch 


t) Ursce Majoria 


Tip of the Great Bear's Tail 2 


i 206° 


50° N 


Alderamin 


a Cephei 


Breast of Cepheus 3 


318° 


62° N 


ViNDEMIATRIX 


e Virginia 


Right Arm of Virgo 3 


194° 


in* n 


Cor Caroli 


a Canum Venaticorum 


The Hunting Dogs 3 


193° 


39° N 


Alcyone 


ij Tauri 


The Pleiades 3 


55° 


23f°N 



Ottestions. — 343. To what extent are star-names used ? Mention some of the prin- 
cipal. 



THE STAES. 241 

PROBLEMS FOR THE CELESTIAL GLOBE. 

Problem I. — To find the place of a constellation or star on 
the globe : Bring the degree of right ascension belonging to 
the constellation or star to the meridian ; and under the 
proper degree of declination will be the constellation or 
star, the place of which is required. 

Note. — The student should he exercised in finding the places of all the 
constellations or stars laid down in the lists, according to this rule. The 
place of a planet or comet may also he found by this rule when its right 
ascension and declination are given. 

Problem II. — To find the appearance of the heavens at any 
place, the hour of the day and the day of the month being given : 
Make the elevation of the pole equal to the latitude of the 
place ; find the sun's place in the ecliptic, bring it to the 
meridian, and set the index to 12. If the time be before 
noon, turn the globe eastward; if after noon, turn it west- 
ward till the index has passed over as many hours as the 
time wants of noon, or is past noon. The surface of the globe 
above the wooden horizon will then show the appearance of 
the heavens for the time. 

Note. — The student must conceive himself situated at the centre of the 
globe looking out. 

Problem III. — To find the declination and right ascen- 
sion of any constellation or star : Proceed in the same 
manner as to find the latitude and longitude of a place on 
the terrestrial globe. 

STAR FIGURES. 

344. Particular stars can be easily recognized in the heav- 
ens by noticing the configurations which they form with 
each other, or by using the more conspicuous stars as 
" pointers ;" that is, by assuming two bright stars so situated 

Qttestiok.— 344. How to find particular 6tars ? 



242 THE STAKS. 

that a straight line drawn through both will point directly 
to the less prominent star whose position it is desired to 
ascertain. 

a. This is sometimes called the method of " alignments," and is 
that usually employed by astronomers. A few examples are here 
given in order to enable the student to find some of the most conspic- 
uous of the stars. 

1. The Great Dipper, or Charles's Wain. — This consists of seven 
bright stars, in the Great Bear, so situated as to resemble a dipper 
with a bent or curved handle, four of the stars forming the bowl, and 
three, the handle. It is situated within the circle of perpetual appari- 
tion, and hence is always visible, although in different positions as it 
revolves around the pole. The two stars at the far side of the bowl 
(a and /3) are called the " pointers" because a line drawn through them 
would reach the pole-star, which can, therefore, always be found by 
discovering the Great Dipper. The pole-star, by modern astronomers 
called Polaris, by the Greeks Cynosura, and by the Arabians Alrucca- 
bdh, is situated about 1^° from the pole, and forms the extremity of 
the upwardly curved handle of a small dipper, which occupies a 
reversed position from that of the Great Dipper, and consists of quite 
faint stars. 

2. Trapezium of Draco. — About 90° east of the Great Dipper are 
four stars so arranged as to form an irregular quadrangle or trapezium. 
These are in the head of Draco, and with another, a little to the west, 
situated in the nose (Bastaben), form almost the letter V, pointing to 
the west. 

3. The Chair of Cassiopeia. — This consists of five stars of the 3d 
magnitude, which, with one or two smaller ones, form the figure of an 
inverted Chair ; it is situated almost precisely at the opposite side of the 
pole from the Dipper, being nearly 180° from it and in about the same 
declination ; it can thus be easily found. 

4. The Great Square of Pegasus. — South of the Chair and a little to 
the west, are four stars about 15° apart, forming a large square. They 
are quite bright stars and the figure is very obvious. The north-eastern 
star is Alpheratz, in the head of Andromeda ; the south-eastern, Alge- 
nib; the south-western, Markab ; and the north-western, Scheat 
Algenib and Alpheratz are on the equinoctial colure, which being con- 
tinued toward the north passes through Caph, in Cassiopeia. 

Questions.— a. What star-figures are described? What is the situation of each? 



THE STARS. 243 

5. The Great Y of Bootes. — This consists of the bright and pecu- 
liarly ruddy star Arcturus, at the lower extremity of the letter ; 
Mirach, at the fork ; Seginus, at the extremity of the western arm ; 
and Alphecca, in Corona Borealis, at that of the eastern. This figure 
is less than 45° to the south-east of the Great Dipper. Arcturus and 
Seginus farm with Cor Garoli, situated toward the west, a large triangle ; 
and a similar but a larger figure is also formed by Arcturus with Dene- 
bola, about 35° west, and Spica Virginis, about as far south. 

6. The Diamond of Virgo is a large and very striking figure formed 
of Cor Caroli and Spica Virginis, at the extremities of its longest 
diagonal, and Arcturus and Denebola at those of the shortest. The 
former are about 50° apart ; the latter 35i°. The figure extends from 
north to south. 

7. The Cross of Cygnus. — This consists of five stars so arranged 
as to form a large and regular cross, the one at the upper extremity 
being Deneb, a star of the first magnitude. This figure is very mani- 
fest and is situated about 35° to the west of the Square of Pegasus. 
The star at the lower extremity of the cross is called Albirco. Deneb, 
or Deneb Cygni {Deneb means tail), is sometimes called Arided. A 
short distance toward the west from the Cross is the bright star Vega, 
forming with two faint stars near it a small triangle, the base being 
turned toward the side of the cross. 

8. The Sickle of Leo. — If the line joining the "pointers "of the 
Great Dipper be continued toward the south, it will pass through a most 
beautiful object, having the complete form of a sickle, the bright star 
Regulus being at the extremity of the handle, and the curve of the 
blade toward the north-east. 

9. The V of Taurus.— This is a group of stars situated in the head 
of the Bull, the brightest of which is Aldebaran, a ruddy star of the 
first magnitude, and situated at the left upper extremity of the letter. 
Aldebaran is an Arabic word and means, " that which follows :" it wrs 
applied to this star because it follows the Pleiades. This group of 
stars is called the Hyades. A little to the north-west is the famous 
cluster of small stars called the Pleiades, said once to consist of seven 
stars, although now we only discover six, of which Alcyone is the 
brightest. 

10. The " Bands of Orion." — These are in a splendid group of 
stars to the south-east of Taurus, and situated under the equinoctial, 
consisting of four brilliant stars in the form of a long quadrangle 



244 THE STAKS. 

intersected in the middle by three stars arranged at equal distances in 
a straight line, and pointing to Sirius, the most splendid star in the 
heavens, on one side, and the Hyades and Pleiades on the other. These 
three stars have been called the " Ell and Yard ;" in the Book of Job 
they are called the Bands of Orion. A line of faint stars projects from 
these toward the south. At the north-east extremity of the quadrangle 
is Betelgeuse ; at the south-east, Saiph; at the south-west, Bigel ; and 
at the north-west, Bellatrix. 

11. The Crescent of Crater. — To the south-east of the Sickle may 
be distinctly seen a beautiful crescent or semi-circle opening toward 
the west, consisting of stars of the sixth magnitude. They form the 
outlines of Crater ; and nearly south of the Sickle is the bright star 
Cor Hydra), almost solitary in the heavens. 

12. The Dipper of Sagittarius. — This is a very striking figure con- 
sisting of five stars of the 3d and 4th magnitudes, forming a straight- 
handled dipper turned bottom upward. It is a considerable distance 
south of Lyra, but comes to the meridian a very short time after it. 
The stars at the mouth of the dipper are about 5° apart. 

Familiarized with these few configurations, it will not be difficult 
for the student, with the assistance of the globe or a planisphere, to 
acquire a knowledge of the other visible stars and their positions in 
the constellations to which they belong. 

345. The appakent places of the stars are constantly 
changing in consequence of the precession of the equinoxes. 
Their right ascensions are increasing at the annual rate of 
50", and their declinations changing as the equinoctial pole 
revolves around that of the ecliptic. 

a. The star Polaris is about 1^° from the pole, and is making a 
constant approach to it ; which it will continue to do until its dis- 
tance is about \°. It will then recede till in about 12,000 years the 
bright star Vega, which is now 51° 20' from the pole will be less than 
5° from it, and will therefore be the pole-star. About 4,000 years ago 
a Draconis was the polar star, being about 10' from the pole. 

346. Nutation. — The precession of the equinoxes is not 
a uniform movement, but is subject to periodical variations 

Questions.— 345. Are the stars absolutely " fixed ?" What change constantly occurs ? 
a. What change in the pole-star ? 346. What is nutation ? How caused ? 



. THE STARS. 245 

occasioned by the different positions of the sun and moon 
with respect to the plane of the equinoctial. When the sun 
is at the equinox its effect is nothing ; at the solstice it is 
at its maximum ; and thus arises, in connection with the 
general revolution of the pole, a vibratory motion of the 
earth's axis, called nutation.* 

347. The solar nutation is very slight and goes through 
all its changes in one year ; but that of the moon, depend- 
ing on the position of its nodes with respect to the earth's 
equinoxes, requires a period of 18^ years. The latter is what 
is ordinarily meant by nutation. 

a. By the lunar nutation alone, the pole of the equator would be 
made to describe, in 18i years, a small ellipse, about 18^" by 13f", the 
longer axis being in the direction of the ecliptic pole ; but being car- 
ried by the general movement of precession round the pole of the 
ecliptic at the rate of 50" annually, it actually moves in a circle the 
circumference of which is an undulating curve, somewhat like the real 
orbit of the moon, the limit of the undulation either way being 9^". 

b. The discovery of the nutation of the earth's axis was made by 
Dr. James Bradley in 1727, by noticing slight variations in the right 
ascensions and declinations of the stars of which neither precession 
nor any other known source of disturbance would account. The true 
cause of the phenomena soon suggested itself to his mind, but could 
not be confirmed until after 18 \ years of observation. It was there- 
fore not announced till 1745. 

348. Aberration. — This is a change in the apparent 
places of " the stars, which arises from the motion of the 
earth in its orbit, combined with the progressive motion of 
light. 

a. This displacement of the stars was first observed by Hooke 
while attempting to discover a parallax in y Draconis ; but the true 
explanation of its cause was given by Dr. Bradley in 1727, — the year 

* Nutation is derived from a Latin word which means a nodding. 

Questions.— 347. Periods of the solar and lunar nutations? a. Effect of the lunar 
nutation ? ft. By whom and how discovered ? 848. What is aberration ? a. How 
and when discovered ? 



246 THE STARS. 

in which the death of Newton took place. It was one of the most 
interesting and important astronomical discoveries ever made, and 
afforded an entire confirmation of the progressive motion of light, dis- 
covered by Roemer about 50 years previously. 

b. Cause of Aberration. — An object is always seen in the direction 
in which the rays of light coming from it strike the eye. Now this 
depends not only on the actual direction of the rays themselves, but 
on our own motion with reference to them ; for if a ray is proceeding 
perpendicularly from an object and we are moving directly across it, it 
will appear to strike against the eye in an oblique direction, and thus 
the object will, in appearance, be thrown forward of its true place, by J 
an angle depending for its size upon the ratio of the velocity of our 
own motion to that of light. This change of direction of the rays of 
light is similar to that which takes place in the drops of rain when 
we are running in a shower, and the rain descends perpendicularly ; for 
then it beats in our faces as it would if we were standing still and the 
wind were blowing it obliquely against us. 

c. Amount of Aberration. — Since the velocity of light is 184,000 
miles a second while that of the earth is but little more than 18 miles, 
the ratio of the latter to the former is about .0001, which is the sine of 
an angle of 20£" ; and this accordingly is the amount of displacement 
due to aberration, when the star is so situated that the rays proceed- 
ing from it are perpendicular to the plane of the earth's orbit, the 
star in that case appearing each year to describe a small circle having 
a radius of 20 £•'. When the rays are oblique to this plane, the circle is 
foreshortened into an ellipse, and the amount of displacement varies, 
being 20^" only when the rays are perpendicular to the earth's motion ; 
while in the case of stars situated in the plane of the ecliptic, there is 
merely an apparent oscillation, in a straight line, amounting to 41" 
during each revolution of the earth. 

d. The phenomena connected with aberration are thus very compli- 
cated ; and as they are all satisfactorily explained by the hypotheses of 
the earth's motion and that of light, both receive a confirmation from 
this important discovery. 

349. The Galaxy, or Milky Way is that faint lumi- 
nous zone which encompasses the heavens, and which,.when 

Questions. — b. Its cause? e." Amount of displacement caused by it? d. What is 
proved by it ? 349. What is the Galaxy or Milky Way ? 



• THE STARS. . 247 

examined with a telescope, is found to consist of myriads of 
stars. Its general course is inclined to the equinoctial at an 
angle of 63°, and intersects it at about 105° and 285° of 
right ascension. Its inclination to the plane of the ecliptic 
is consequently about 40°. 

a. This nebulous zone is of very unequal breadth, not exceeding in 
some parts 3° ; while in others it is 10° or even 16° ; the average 
breadth being about 10°. It passes through Cassiopeia, Perseus, 
Gemini, Orion, Monoceros, Argo, the Southern Cross, Centaurus, Ophiu- 
chus, Serpens, Aquila, Sagitta, Cygnus, and Cepheus. From a Centauri 
to Cygnus it is divided into two parts, the whole breadth including the 
two branches being about 22°. It exhibits other divisions at several 
points of its course. 

350. Its appearance is not uniform, some parts being 
exceedingly brilliant ; while others present the appearance of 
dark patches, or regions comparatively destitute of stars. 

a. Near the Southern Cross, where its general appearance is most 
brilliant, there occurs a singular dark, pear-shaped space, obvious to 
the most careless observer. To this remarkable patch the early navi- 
gators gave the name of the coal-sack. A similar vacant space occurs in 
the northern hemisphere at Cygnus. 

b. The number of stars in the Milky Way is inconceivably 
great. Sir William Herschel states that on one occasion he calculated 
that 116,000 stars passed through the field of his telescope in a quarter 
of an hour, and on another tnat as many as 258,000 stars were seen to 
pass in 41 minutes. The total number, therefore, can only be esti- 
mated in millions. Struve's estimate of the whole number visible in 
Sir William Herschel's great reflecting telescope is 20£ millions ; and 
the number brought into view by the still more powerful instrument 
of Lord Rosse must be very much greater. 

351. The prevailing theory with regard to the Milky 
Way is, that it is an immense cluster of stars having the gen- 
eral form of a mill-stone, split at one side into two folds, or 

Questions. — Its position ? a. Its breadth ? What constellations does it pass through ? 
850. Appearance of the Milky Way ? a. The " coal-sack ?" 6. Number of stars in 
the Galaxy? 351. What is it supposed to be ? Its figure ? 



248 THE STARS. 

thicknesses, inclined at a small angle to each other; that all 
the stars visible to us belong to this system ; and that the 
sun is a member of it and is situated not far from the mid- 
dle of its thickness, and near the point of its separation. 

a. The fact that the Milky Way is composed of vast numbers of 
stars was conjectured by Pythagoras and other ancient astronomers, 
but was not positively discovered till Galileo directed his telescope 
to the heavens. The hypothesis that it is a vast cluster of which the 
sun and visible stars are members, was first suggested by Thomas 
Wright in a work entitled the " Theory of the Universe," published 
in 1750. This subject received a careful and prolonged investigation 
by Sir William Herschel, the results of which he published in 1784, 
and which seems to establish the hypothesis mentioned in the text. 
This opinion he arrived at by taking observations at different distances 
from the zone of the Galaxy, and counting the stars within the field of 
view. On the supposition that the stars are uniformly distributed 
throughout the system, the number thus presented would indicate the 
extent of the cluster in the direction in which they were seen ; and in 
this manner some general idea of its form would be obtained. 

b. Galactic Circle and Poles. — The extensive survey made by 
Sir William Herschel of the stars in the northern hemisphere, and con- 
tinued by his son, Sir John Herschel, in the southern, has proved that 
there are two points of the celestial sphere, diametrically opposite to 
each other, at which the stars are very thinly scattered ; while at and 
near the circle of which these are the poles the stars are so densely 
crowded as to be absolutely countless. This circle lies very near the 
middle course of the Milky Way, and hence is called the Galactic 
Circle ; the points at which the stars are least dense are called the 
Galactic Poles. It is also found that the decrease of the density of 
the visible stars in proceeding either way from the plane of the 
Galactic Circle conforms to the same law, but that the density in the 
southern hemisphere is at each latitude greater than at the correspond- 
ing latitude in the northern. 

The annexed figure represents the general form of a section of this vast 
cluster, or stratum of stars, S being the place of the sun ; S/, the position 
of the plane of the Galactic Circle; bb, the Galactic Poles. It will be 

Questions. — a. By whom was this theory first suggested ? Herschel 1 s investigations ? 
Mode of estimating its form ? b. What are the Galactic circle and poles ? How found ? 



THE STABS. 249 

obvious that at the visual lines Se and S/ the stars must appear most 
dense, and at S6 least ; while at intermediate points, the density will vary 
with the obliquity of the visual lines ; and as S/ is nearer the northern 
confines of the stratum than the southern, more stars must be visible in 

Fig. 117- 



SECTION OP THE GALACTIC STRATUM. 

the southern hemisphere than in the northern ; the number of stars depend- 
ing in each direction upon the length of the visual line. The apparent 
separation of the Milky Way is accounted for by supposing the sun to be 
placed, as indicated, near the point where the two branches diverge. 

c* Dimensions of the Galactic System. — The thickness of this 
stratum of stars Herschel supposed to be about 80 times the distance 
of the nearest star from the solar system ; but that its extreme length 
is equal to 2,000 times that distance. To move from one extreme point 
of this vast space to the other, light would require about 7,000 years. 

352. Proper Motion of the Stars. — The stars do not 
always remain precisely in the same places with respect to 
each other, but in long periods of time perceptibly change 
their relative positions, some approaching each other, and 
others receding. This apparent change of position is called 
their proper motion. 

a. The first astronomer to whom the idea of a proper motion of the 
stars (that is, a motion of the stars themselves, independent of annual 
parallax) occurred was Halley. Comparing the anciently recorded places 
of Sirius, Arcturus, and Aldebaran with their positions as observed by 

Qtxestions. — c. Dimensions of the Galactic System ? 352. What is the proper mo- 
tion of the stars ? a. How found? 



250 THE STAES. 

himself in 1717, and making every allowance for the variation in the 
obliquity of the ecliptic, he still found differences of latitude amount- 
ing to 37', 42', and 33', respectively, for which he could not account, 
except on the supposition that the stars themselves had changed their 
positions. This was confirmed by Cassini in 1738, who ascertained 
that Arcturus had apparently moved 5' in 152 years, while the neigh- 
boring star i) Bootis had been nearly if not quite stationary. The star 
61 Cygni has a considerable proper motion, having changed its position 
in fifty years nearly 4y. 

b. Motion of the Solar System in Space. — In 1783, Herscliel 
undertook the investigation of this interesting subject ; and finding 
that in one part of the heavens the stars approached each other, while in 
the opposite part their relative distances seemed to increase, he arrived 
at the conclusion that this apparent change in the stars is caused by a 
real motion of the solar system in space. For, evidently, if we are 
in motion, the stars toward which we are moving will open out, while 
those from which we are receding will appear to come together; and 
as it was observed by Herschel that the stars in the constellation 
Hercules are gradually becoming wider and wider apart, he inferred 
that the motion of the sun and its attendant planets is in that direc- 
tion. The mean result of the observations of Herschel, and several 
distinguished astronomers who in more recent times have investigated 
the subject, is that the point toward which the solar system is moving 
is in 260° 20' of right ascension, and 33° 33' of north declination, 
which agrees very nearly with that reached by Herschel himself. The 
annual angular displacement of a star situated at right angles to the 
direction of the sun's motion and at the mean distance of stars of the 
first magnitude, is computed at about %" ; and therefore the velocity 
of the motion is estimated at about 160 millions of miles in a year. 

e. Central Sun. — The hypothesis that the solar system is revolving 
around a central sun was first suggested by Wright in 1750. Madler 
supposed that the central sun is the star Alcyone in the Pleiades ; but 
it is not thought by astronomers that sufficient evidence exists for this 
hypothesis. All that can be said to be established is, that the sun with 
its great retinue of revolving worlds is moving in space toward a point 
in the constellation Hercules. 

353. Multiple Stars are those which to the naked eye 

Qttestionb.— ft. What motion has the solar system? How indicated? To what 
point is it moving ? e. Central sun ? 853. What are multiple stars? Double stars? 



THE STARS. 251 

appear single, but when viewed through a telescope are 
separated into two or more stars. Those that consist of two 
stars are called double stars. 

a* Double stars differ much in their distance from each other ; in 
some cases being so near as to be separated only by the most powerful 
telescopes ; in others, they are as much as \' from each other. These 
stars were carefully observed by Sir William Herschel, and have 
received much attention from the distinguished astronomers of more 
recent times. The list of this class of stars now contains upward of 
six thousand, classified according to their angular distances from each 
other. 

b. The members of a double star are generally quite unequal in 
size. The pole-star consists of two stars of the second and ninth mag- 
nitude respectively, and about 18" apart ; Rigel has a companion star 
about 10" from it, and of the ninth magnitude; Castor consists of 
two stars of the third and Fig. 118. 

fouth magnitudes about 5" 

apart ; y Virginis (Gamma 

of the Virgin) is a very 

remarkable star consisting 

of two stars each of the 

fourth magnitude. (See 

Fig. 118.) c Lyrse (Epsilon 

.Ji 4/. T „ \ i*. „~ ^„„,v,wi„ 1. pole-stab; 2. eigbl; 3. castob; 4. y yibgixib. 

of the Lyre) is an example 

of a star consisting of two stars each of which is double, being thus a 

double-double star. In 1862, Sirius was discovered, by Mr. Alvan 

Clark, of New York, to have a minute companion star situated about 

7" from it. 

c. Colored Stars. — There is considerable diversity in the color of 
both the single and double stars. Thus Vega, Altair, and Spica are 
white ; Aldebaran, Arcturus, and Betelgeuse, ruddy ; Capella and Pro- 
cyon, yellow. Single stars of a fiery red or deep orange are not 
uncommon ; but among the conspicuous stars there is only one 
instance (/? Librae) of a green star, and none of a blue one. Many 




Questions.— a. Apparent distance of double stars? 6. Comparative size and color f 
Size of the members of double stars ? Examples ? c. Difference in the color of single 
stars ? Of double stars ? Complementary colors ? Presented by how many stars J 



252 THE STARS. 

double stars exhibit the beautiful and curious phenomena of comple- 
mentary colors,* the larger star being usually of a ruddy or orange 
hue, and the smaller one, green or blue. In some cases, this is found 
to be the effect of contrast ; since, when a very bright object of a par- 
ticular color is viewed with another less brilliant, the latter, although 
in reality white, appears to have the complementary color of the former. 
In this way a large and bright yellow object will cause other objects 
to seem violet ; and crimson, produce the effect of green. In many 
cases, however, there seems to be a real difference in the color of the 
constituents of double stars ; for when one of them is concealed by 
introducing a slide in the telescope, the other still retains its color. 

Of 598 bright double stars contained in Struve's catalogue, 120 pairs 
are of totally different hues. The number of reddish stars is double 
that of the bluish stars ; and that of the white stars 2\ times as great as 
that of the red ones. 

d. That some stars have changed in color is an established fact. 
Ptolemy and Seneca expressly declare that Sirius was of a reddish hue ; 
whereas now it is of a brilliant white. Stars described by Flamstead 
were found by Herschel to have changed in this respect ; and y Leonis 
and 7 Delphini have changed since his time. 

354. Bikaby stars are double stars one of which revolves 
around the other, or both revolve around their common cen- 
tre of gravity. 

a. History of the Discovery,~-The discovery of this connection 
between the constituents of double stars was, perhaps, the grandest of 
Sir William HerscheTs achievements. It was announced by him in 
1803, after twenty-five years of patient observation, which he com- 
menced with the view to discover the stellar parallax by noticing 
whether any annual change in the relative positions of double stars 
existed. To his astonishment, he found from year to year a regular 
progressive movement of some of these bodies, indicating that they 
actually revolve one round the other in regular orbits, and thus that 



* Complementary colors are those which being blended produce white. 
They are red, yellow, and Hue. The complementary color of any one of 
these is a combination of the other two. Thus orange is complementary of 
blue ; and green, of red. 

Qtxestions. — d. Change of color in stars? 854. What are binary stars? a. How- 
discovered ? 






THE STABS. 



253 



the law of gravitation extends to the stars. These stars are called 
Binary* Stars, or Systems, to distinguish them from other double stars 
which, although perhaps at immense distances from each other, ap- 
pear in close proximity, because, as viewed from the earth, they are 
very nearly in the same visual line, and therefore are said to be 
optically double. 

355. The observations of Herschel resulted in the dis- 
covery of about 50 binary stars ; but since bis time the 
number has been, according to Madler, increased to 600. 
Most of tbe double stars are believed to be binary systems. 

356. Oebits and Periods of Binary Stars. — A very 
careful scrutiny of these bodies and their changes in posi- 
tion has shown that they revolve in elliptical orbits of con- 
siderable eccentricity and in periods greatly varying in length. 

The following is a list of the most remarkable of these bodies, with 
their periods, and the semi-axes and eccentricities of their orbits : 



Name. 


Period. 


Semi-Axis 
Ma jo p. 


Eccentricity. 




Years. 


" 




C Herculis, 


36.3 


1.25 


0.44 


ij Coronse Borealis, 


43.6 


0.95 


0.28 


Sirius, 


49. 


7.05 




C Cancri, 


58.9 


1.29 


0.23 


\ Ursse Majoris, 


63.1 


2.45 


0.39 


a Centauri, 


75 3 


30. 


0.96 


u Leonis, 


84.5 


0.85 


0.64 


70 Ophiuchi, 


92.8 


4.19 


0.44 


y Coronse Australis, 


100.8 


2.54 


0.60 


f Bootis, 


117.1 


12.56 


0.59 


6 Cygni, 


178.7 


1.81 


0.60 


t) Cassiopeise, 


181. 


10.33 


0.77 


y Virginis, 


182.1 


3.58 


0.87 


a Coronae Borealis, 


195.1 


2.71 


0.30 


Castor, 


252.6 


8.08 


0.75 


61 Cygni, 


452. 


15.4 




/z Bootis, 


649.7 


3.21 


0.84 


7 Leonis, 


1200. 







* From the Latin word bini, meaning two by two. 



Questions. — 355. How many discovered ? 356. Their orbits and periods ? 



254 



THE STARS. 



It will be observed from the preceding table that the eccentricities of 
these orbits are as great as those of the comets. 

b. Dimensions of Stellar Orbits. — In this table the semi-axis is 
given as seen perpendicularly from the earth ; but to find the actual 
dimensions of the orbit, the parallax must be ascertained. The 
problem is then a simple one. Thus, the semi-axis of a Centauri is 
30" ; but since its parallax is 0.9187", 1" must at that distance sub- 
tend more than the semi-axis of the earth's orbit in the proportion 
of .9187 to 1 ; that is, it must be 1.088 ; and 30" must subtend 
1.088 X 30 = 32.64 times the semi-axis of the earth's orbit, which 
is equal to about 3,000 millions of miles. Now, the eccentricity 
is .96 ; and therefore the nearest distance to the central star is only .04, 
or 120 millions, while the farthest distance is 5,880 millions. In the case 
of 61 Cygni, the semi-axis is 15.4", while the parallax is 0.3638" ; hence, 
1" subtends at its distance 1 -h.3638 = 2.75 (nearly) ; therefore the 
semi-axis 2.75 X 15.4 = 42.35 times the semi-axis of the earth's orbit, 
which is equal to 3,875 millions of miles. 

c. The following list contains all the stars whose parallax has teen 
found : 



Name. 


Pakallax 


Name. 


Parallax 


a Centauri, 


0.9187 


a Lyrae, 


0.155 


61 Cygni, 


0.5638 


Sirius, 


0.150 


21258 Lalande, 


0.2709 


i Ursae Majoris, 


0.133 


17415 Oeltzen, 


.247 


Arcturus, 


0.127 


1830 Groombridge, 


.226 


Polaris, 


0.067 


70 Ophiuchi, 


.16 


Capella, 


0.046 



d. Masses of the Stars. — The joint mass, and in some cases the 
separate masses, of each pair of revolving stars can be ascertained, 
when we know their period and distance from each other. Thus, taking 
Sirius for example, we find its distance from its companion star to be 
47 times the earth's distance from the sun, while its period is 49 times 
as great as the earth's. Hence, by the law stated in Art. 306, a, the 



Questions. — b. Size of orbits — how found? The calculation? c. What is the 
nearest fixed 6tar ? Parallax of Sirius ? What distance does it denote ? Capella ? 
d. Masses of the stars— how calculated ? 



THE STABS. 255 

mass of the sun being 1, that of Sirius and its companion is 47 s -*- 49 s 
= 43.25. Now, it has been discovered* that Sirius is situated at a dis- 
tance from the centre of gravity of both revolving stars equal to 16^ 
times the earth's distance from the sun ; and therefore the companion 
star is 47 — 16^ = 30| that distance ; and as their masses are in inverse 
proportion to their distances from the centre of gravity, the mass of 
Sirius is to that of its satellite a3 30f to 16£, or as 123 to 65. Conse- 
quently, the mass of Sirius is iff X 43i = 28.3 times th e ma ss of the 
sun ; and, if the densities are the same, its diameter is V28.3, or a lit- 
tle more than three times that of the sun, and its disc 9 times as great. 
But photometric measurements have shown that its light is 400 times 
as great as that of the sun would be if the latter were removed to the 
distance of Sirius ; so that the materials of this star must be much 
less dense, or its light intrinsically far more brilliant, than that of the 
solar orb. 

e. The Sun a Small Star. — By certain photometric comparisons 
recently made by Messrs. Clark and Bond between the star Vega 
(a Lyrae) and the sun, it has been shown that if the latter body were 
removed to 133,500 times its present distance, it would send us the 
same quantity of light as the star. But the nearest star (a Centauri) 
is more than 200,000 times as far from us as the sun ; and Vega, about 
six times as far as a Centauri. Hence the sun, if removed to the dis- 
tance of the nearest star, would shine only as a star of the second 
magnitude ; and if removed to the mean distance of stars of the first 
magnitude, would appear as a star of the sixth magnitude, and be just 
visible to the naked eye. It would seem therefore that the sun, mag- 
nificent luminary as it appears to us, is only one of the smallest or 
least brilliant of the stars. 

357. Physical Constitution of the Stabs. — An analy- 
sis of the light of the stars indicates that they consist of 
solid incandescent matter surrounded with an atmosphere 
containing the vapor of some of the elementary substances 
existing on the earth ; such as mercury, antimony, sodium, 
hydrogen, etc. 

a. Spectrum Analysis. — The band of rainbow colors, called the 

* By Mr. Safford, of Chicago. 

Questions. — e. Is the sun a large or a small star ? 357. Physical constitution of the 
stars ? How indicated ? a. Spectrum analysis — what is it ? How was the method 
discovered ? 



256 THE STARS. 

solar spectrum, produced by causing the sun's rays to pass through a 
piece of triangular glass called a prism, was noticed as early as 1802, 
by Wollaston, to be crossed by dark bands or lines ; and in 1815, 
Fraunhofer, by examining the spectrum with a telescope, discovered 
as many as 500 of such lines, and since then the number perceived has 
increased to thousands. Now, it has also been observed that, when 
the light of any inflamed vapor passes through a prism, its spectrum 
consists of one or more bright-colored bands, differing in number, 
relative position, and color, according to the substance from which the 
vapor proceeds ; but that when the light of any incandescent but not 
vaporized substance is made to pass through the inflamed vapor, the 
bright-colored lines are immediately changed to dark lines, the vapors 
absorbing from the light the same kind of rays which they themselves 
emit. Hence it is inferred that the substances whose peculiar lines are 
found in the solar spectrum are contained in a vaporous condition in 
the solar atmosphere, and as many as fourteen have been already iden- 
tified. The stellar spectra also exhibit similar dark lines, each star 
having a peculiar series of them ; and some are recognized as produced 
by the burning of substances found on the earth. Thus, some of the 
metals are found in some of the stars, and others in other stars ; and 
this is thought to account for the different colors which the stars pre- 
sent. Sirius has been discovered to have five of our elements ; and 
Aldebaran, nine. 

358. Stars that appear double when viewed through an 
ordinary telescope are often separated by more powerful 
instruments, into triple, quadruple, or other multiple stars. 

Fig. 119. a. Examples are furnished by 

the following stars : e Ly rae, already 
referred to, which consists of two 
stars, each of which is double ; 
C Cancri (Zeta of the Crab), com- 
posed of three stars, two large and 
one small ; d Orionis (Theta of 
Orion), a very remarkable star, 
consisting of four bright stars, 
two of which have small compan- 
o oeionis. tkapkzium op orion. ion stars, thus forming a sextuple 

Questions.— 353. What are triple stars, etc. a. Examples? Trapezium of Orion ? 




THE STAES. 257 

star. From the configuration of the four principal stars this is 
sometimes called the trapezium of Orion. (See Fig. 119.) As all these 
stars have the same proper motion, they are believed to constitute 
one system. It is said that a seventh star belonging to this system 
has been discovered by Mr. Lassell. 

359. Vakiable stars are those which exhibit periodical 
changes of brightness. The number of such stars discov- 
ered up to the present time (1867) is about 120. They are 
sometimes called Periodic Stars. 

a. Examples. — One of the most remarkable of these stars, and the 
first noticed (by Fabricius in 1596), is Mira — the wonderful — in the 
Whale (o Ceti). It appears about 12 times in 11 years ; remains at its 
greatest brightness about a fortnight, being equal to a star of the 2d 
magnitude; decreases for about 3 months, and then becomes invisible, 
remaining so 5 months, after which it recovers its brillancy ; the period 
of all its changes being about 331^ days. 

Algol (/3 Persei) is another remarkable variable star of a very short 
period, it being only 2 d 20 h 49 m . It is commonly of the 2d magnitude, 
from which it descends to the 4th magnitude in about 3£ hours, and 
so remains about 20 minutes, after which in 3i hours, it returns to the 
2d magnitude and so continues 2 d 13 h , when similar changes recur. 
Observation shows that the period of Algol is less than it was in for- 
mer years. Its variability was first noticed in 1669. 6 Cephei is 
remarkable for the regularity of its period, which is 5 d 8 h 47 m . Betel- 
geuse, one of the four stars in the great quadrangle of Orion, has a period 
of 200 days. There is a star in Cygnus the variations of which are 
effected in 406 days. Three of the seven stars of the Great Dipper in 
Ursa Major are variable stars, their periods extending over several 
years. The double star y Virginis is also variable, its two component 
stars having changed in brightness, the most brilliant becoming infe- 
rior to the other, a Cassiopese is also variable as Well as double ; and 
there are several others. According to Mr. Hind, the color of most 
variable stars is ruddy. 

b. Cause of Variable Stars. — Several hypotheses have been sug- 
gested to account for these interesting phenomena. One is that these 
bodies rotate and thus present sides differing in brightness, or obscured 

Qxtestions. — 359. "What are variable stars? How many discovered? a. Mira? 
Algol ? Other examples ? 6. Cause of variable stars ? 



258 



THE STARS. 



by spots similar to those which are seen on the solar disc ; another, that 
their light is obscured by planets revolving around them ; and a third, 
that their light is diminished by the interposition of nebulous masses, 
since it has been observed that during their minimum brightness they 
are often surrounded by a kind of cloud or mist. No one of these 
hypotheses is entirely satisfactory, and hence we may conclude that 
the true cause of the variability of these stars is unknown. 
c. The following is a list of the most interesting of these bodies : 



Name. 


Period. 


Changes 
of Magn. 


1 

Name. 


Pebiod 


Changes 
of Magn. 




Days. 


From to 




Days. 


From to 


(3 Persei, 


2.86 


2i 4 


a Herculis, 


88£- 


3 4 


6 Cephei, 


5.36 


4 5 


o Ceti, 


33H 


2 


r\ Aquilse, 


7.17 


3± 4i 


v Hydrae, 


449£ 


4 10 


(3 Lyrae, 


12.9 


3* 4£ 


rj Argus, 


46 yrs 


1 4 



360. Temporary stars are those which suddenly make 
their appearance in the heavens, sometimes shining with 
very great brilliancy; and, after a while, gradually fade 
away, either entirely disappearing or remaining as faint 
telescopic stars. The latter are properly called New Stars. 

a. Ancient Instances. — The first on record was observed by Hip- 
parchus, in the second century B.C. ; and it was the appearance of this 
star that prompted him to make a catalogue of the stars, — the first 
ever executed. This star seems to have been noticed also by the 
Chinese, as its appearance is mentioned in their chronicles under the 
date of 134 B.C. Brilliant stars appeared in or near Cassiopeia in the 
years 945 and 1264 A.D. 

b. Star of 1572. — This was a very remarkable one, and is described 
by Tycho Brahe, who observed it attentively. It appeared first as a 
star of the first magnitude, blazing forth with the lustre of Jupiter or 
Venus, and occasioning the greatest astonishment not only to scien- 
tific men, but to the common observers. For a while it was visible 



Questions.— c. The most remarkable of these stars? 360. What are temporary 
stars? New stars? a. Ancient instances ? 6. Tycho's star? 



THE STABS. 259 

even at noon. It lasted from November, 1572, to March, 1574, — 17 
months. Its color was successively white, yellow, red, and white 
again ; and its position in the heavens was the same during the whole 
time it remained visible. This star is supposed to be identical with 
those which appeared in 945 and 1264, all three being in fact apparitions 
of a variable star of a long period ; and some astronomers regard all 
temporary stars as of this character. 

c. Other Examples. — In 1604 a very splendid star, remarkable for 
its vivid scintillation, shone forth in the constellation Ophiuchus, 
and lasted 15 months. This star was observed by Kepler and Galileo. 
In 1670 a star appeared in Cygnus, which attained the 3d magnitude 
and was visible for about two years, blazing out suddenly a short time 
before its final disappearance. On April 28th, 1848, a new star of the 
5th magnitude was discovered in Ophiuchus, which in a few weeks 
rose to the 4th magnitude, but subsequently dwindled to the 12th mag- 
nitude, and still remains as a telescopic star. Lastly, a new star was 
seen in May, 1866, in Corona Borealis. It first appeared of the 2d 
magnitude, and of a pure white color ; but in a week had changed to 
the 4th magnitude, and a month afterward diminished to the 9th, 
"It is worthy of especial notice," says Sir John Herschel, "that all the 
stars of this kind on record, of which the places are distinctly indi- 
cated, have occurred in or close upon the borders of the Milky Way." 

d. Cause of Temporary Stars. — No satisfactory hypothesis has as 
yet been advanced to account for these phenomena. Some have sup- 
posed that these stars are revolving in elliptical orbits of great 
eccentricity so that they sometimes approach very near us, and then 
recede to great distances ; but this is rendered improbable by the sud- 
den changes in brilliancy ; since, to pass from the first to the second 
magnitude, it is computed by Arago, would require six years, if the 
star moved with the velocity of light ; whereas, that of 1572 underwent 
this change in one month, and that of 1866 diminished to the extent 
of five magnitudes in the same time. Another hypothesis is, that 
extensive conflagrations take place on the surface of these bodies, 
which in their progress give rise to the observed changes in color and 
brightness, and at their extinction leave the body in an obscure state. 
The latter hypothesis has received some support from the recent inves- 
tigations made by Huggins, Miller, and others, by means of the 
spectrum analysis ; for the light of the star of 1866 was shown by 

Questions. — c. Kepler's star? Others? d. Cause of temporary stars ? 



260 THE STARS. 

these experiments to proceed from matter in the state of luminous gas, 
chiefly hydrogen. Hence it is supposed that, by some great convulsion, 
large quantities of gas were evolved from the star, that the hydrogen 
was burning in combination with other elements, and that the inflamed 
gas had heated to incandescence the solid matter of the star. This 
hypothesis does not involve the necessity of destruction ; but, as 
remarked by Humboldt, only " a transition into new forms, determined 
by the action of new forces. Some stars which have become obscure, 
may again suddenly become luminous, by the renewal of the same 
conditions which, in the first instance, developed their light." 

361. Numerous instances are on record of stars formerly 
known to exist which have entirely disappeared from the 
heavens. These are called Lost or Missing Stars. 

a. Examples. — Several of the stars in the catalogue of Ptolemy 
were not to be found in 1433, when the catalogue of Ulugh Beigh was 
made at Samarcand ; and it is now known that 4 stars in Hercules 
have disappeared, 1 in Cancer, 1 in Perseus, 1 in Pisces, 1 in Hydra, 1 
in Orion, and 2 in Coma Berenices. Sir William Herschel recorded in 
1781 the star 55 Herculis ; but nine years afterward it was invisible, and 
has never been seen since. In 1670, it was remarked by Montanari, a 
distinguished astronomer, " There are now wanting in the heavens two 
stars of the 2d magnitude in the stern and yard of Argo. I and others 
observed them in 1664, but in 1668, not the least glimpse of them was 
to be seen." 

b. Why Stars Disappear. — Some of the instances mentioned by 
early astronomers, of lost stars may be the result of erroneous entries ; 
but those of later times can not possibly be accounted for in this way. 
Revolving in orbits, they may have passed beyond the reach of the 
most powerful telescope ; or they be obscured by the interposition of 
great nebulous masses, and thus are only concealed for a certain period, 
which however may comprise hundreds, or even thousands of years. 

362. Star-Clusters. — These are dense masses of stars so 
crowded together, and so far distant, that they present a 
hazy, cloud-like appearance, similar to that of the Milky 
Way. 

Questions. — 361. Lost stars ? a. Examples ? b. Why do stars disappear ? 36?. 
What are star- clusters ? 



THE STARS. 261 

a. Collections of stars visible as such to the naked eye, although 
considerably crowded, are called star-groups. Such are the Pleiades, 
the Hyades, and the group which constitutes the constellation Berenice's 
Hair. The first of these is a well-known object consisting of six stars 
when viewed by the naked eye, but exhibiting about 80 to the tele- 
scope. Seven of these stars have received special names, Alcyone 
being the brightest. 

363. Among star-clusters, a very small number are suffi- 
ciently bright to be distinguished by the naked eye ; but 
generally they require a telescope to render them visible. 

a. Between the Fig. 120. 

bright stars in Cassi- 
opeia and Perseus, 
there is a visible clus- 
ter, one of the most 
glorious objects in the 
heavens. (Fig. 120.) 
The remarkable group 
called Prwsepe, or the 
" Beehive," is another 
example of a cluster 
visible without a tele- 
scope, but only as a 
spot of cloud It is cLtrsTER m pebsetjs. 

situated in Cancer. 

364. The prevailing form of the telescopic clusters is 
circular, with a gradual condensation of the luminous points 
toward the centre, indicating probably that the real form 
is that of a globe. Some of the clusters when viewed 
through powerful telescopes assume a much more irregular 
appearance, although their general form still appears to 
be spherical. Very irregular clusters are rare. 

a. Examples. — A remarkable cluster surrounding the star Kappa 



Questions. — a. Star- groups? Examples? 363. Are star-clusters visible to the 
naked eye? a. Examples? 364. Prevailing form of clusters ? a. Remarkable clusters ? 




262 



THE STARS. 




of the Southern Cross 
consists in part of colored 
stars; and another in the 
southern hemisphere is 
composed entirely of blue 
stars. The one situated 
between Eta and Zeta in 
the constellation Hercu- 
les is a peculiarly mag- 
nificent object in our 
northern heavens on fine 
nights, and is visible to 
the naked eye as a very 
small nebulous spot or 
faint star. In the tele- 
scope its general appear- 
ance is considerably 
clusteb in nEBcuLEs.— Sir J. Herschel. changed by the addition 

of several outlying branches. This splendid object is represented in 
Fig. 121, in which its remarkable condensation at the central portions 
is strikingly exhibited. Very many objects of a similar character are 
visible in different parts of the heavens. 

b. These globular clusters are supposed to be held together by their 
motions and mutual attractions. That there must be a real conden- 
sation is obvious from a simple glance at such an object as that depicted 
in Fig. 121 ; since the increase of brightness toward the centre is far 
too great to be explained on the supposition that the stars are equally 
distributed, but appear closer together at the centre, because the visual 
line traverses there a much greater portion of the mass. 

c. The number of stars contained in these clusters is very great. 
According to Arago, many clusters contain at least 20,000 collected 
in a space, the apparent dimensions of which are scarcely a tenth as 
large as the disc of the moon. The clusters are not equally distrib- 
uted over the heavens, but are most numerous in the Milky Way ; 
while globular clusters most abound in that region of the Galaxy 
contained between Lupus and Sagittarius in the southern hemisphere. 



Questions. — h. Cause of the globular form? Are the stars equally distributed ? c. 
Number of stars in a cluster ? Are the clusters cqially distributed ? . 



CHAPTER XIX. 



NEBULJ. 

365. Nebuljb are certain faintly luminous appearances in 
the heavens, resembling specks of cloud or mist, some just 
visible to the naked eye, but the greater part only to be 
discerned with a telescope. They resemble in their general 
aspect the distant star-clusters, but their physical structure 
appears to be very different. 

366. Their distance from us must be immense, since 
they constantly maintain very nearly the same situation 
with respect to each other and to the stars. Their magni- 
tudes also must be inconceivably vast. 

a. History of their Discovery, — It is only in quite recent years 
that any distinction could be positively made between nebulae * proper 
and those immense star-clusters which present a nebulous appearance 
on account of their great distance. The first of these objects mentioned 
in the annals of astronomy was discovered in 1612, by Simon Marius, 
a German astronomer. This was the nebula situated in the girdle of 
Andromeda. In 1656, Huyghens discovered the great nebula in Orion, 
which he compared to an " opening in the heavens through which a 
brighter region beyond was visible." In 1716, Halley could enumerate 
only six, to which he added a few by his own discoveries ; and during 
the next half century, the number was augmented to about 100. The 
labors of Sir William Herschel, directed to the investigation of this 
department of astronomy for more than twenty years, enabled him in 

* Nebula is a Latin word meaning a little cloud. Plural, nebulae. 

Questions.— 365. What are nebula ? 366. Their distance from us ? a. When and 
by whom discovered ? 



264 NEBULAE. 

1802 to publish a catalogue of 2,500 nebulae and clusters ; and the 
subsequent researches of his son, Sir John Herschel, in the southern 
hemisphere has increased this number to more than 5,000. Very great 
additions, however, have been made to our knowledge of these inter- 
esting objects by the labors of Lord Rosse, aided by the largest 
reflecting telescope ever constructed, and by the application of the 
spectrum analysis. 

367. Nebulae are distinguished from clusters by not being 
resolved into stars when viewed through the most powerful 
telescopes, presenting the appearance of diffuse luminous 
substances, filling vast regions of space, and differing in 
form, and degree of condensation. 

a. Resolvable and Irresolvable Nebulae. — Herschel at first 
thought all nebulae resolvable into stars ; but his subsequent investi- 
gations convinced him that this was an error ; and he accordingly 
divided these objects into resolvable and irresolvable nebula ; the first 
being those vast star-clusters which exhibit a nebulous, or cloudy 
aspect, because of their comparatively crowded condition and great 
distance from us ; and the second, according to his conceptions, im- 
mense aggregations of self-luminous matter, of great tenuity, but 
gradually condensing into solid bodies like the sun and stars. This 
bold conception of Herschel's had been entertained by Tycho Brahe 
and Kepler, who suggested that the new stars seen in their time were 
caused by aggregations of the ethereal matter filling space. The 
first discoverers of the nebulae also noticed an essential difference 
between the light of these great phosphorescent masses and that of 
the stellar clusters, fancifully comparing the former to glimpses of the 
empyrean disclosed by rents or chasms in the celestial vault. Laplace 
applied this conjecture of Herschel's, under the name of the " Nebular 
Hypothesis " to the solar system, in order to explain the manner of its 
evolution. (See page 202.) Many of the irresolvable nebulae of Sir 
William Herschel having been resolved by the great telescope of Lord 
Rosse, or having given indications of being resolvable into stars, the 
opinion came to be almost universally entertained that all nebula) are 
star-cl asters, some so distant that light requires millions of years to 
pass from them to us. But the spectrum analysis has proved this to 

Questions.— 367. How distinguished from clusters ? a. How has this distinction 
been established ? 



nebulj;. 



2C5 



be erroneous, by showing that these luminous masses consist of 
gaseous, not solid matter ; so that Herschel's hypothesis would seem to 
be established. These diffuse and attenuated substances constitute 
thus a peculiar class of objects in the starry heavens, and are the 
nebula denned in the text, although some astronomers still continue to 
classify them with the clusters which have a nebulous appearance. 

368. Nebulae abound chiefly in those regions of the 
heavens in which the stars are least numerous, that is, in 
the vicinity of the Galactic Poles, and are more uniformly 
spread over the zone, which surrounds the South Pole. 
Where stars are excessively abundant, nebulae are rare. 

a. Herschel found this rule to be without exception ; and whenever, 
during a brief interval, no star passed into the field of his telescope, 
as in the diurnal motion the heavens swept by it, he was accustomed 
to say to his secretary, " Prepare to write : nebulae are about to arrive." 

3G9. Nebulae may be divided, according to their form, 
into the following six classes; namely, elliptic, annular, 
spiral, planetary, stellar, and irregular nebulm. 

370. Elliptic nebula are such as Fi s- 122 - 

have the elliptical or oval form. They 
are quite numerous and are of various 
degrees of eccentricity. 

a. Examples. — The most noted of these 
nebulas is that in the girdle of Andromeda, 
already referred to as the first discovered. It 
is one of the grandest and least resolvable in 
the heavens, and is quite visible to the naked 
eye ; so much so, indeed, that it is strange none 
of the ancient astronomers ever observed it. 
Figure 122 exhibits it as drawn by some 
observers with two stars at the extremities of 
the longest diameter. In very powerful tele- 
scopes, such as that at Cambridge, Mass., it 

.,.,..- ,Y . .' „ ELLIPTIC NEBtTLA IK AN- 

presents some quite striking peculiarities of dbomeda. 




Questions.— 368. Where are nebulae abundant ? a. Herschel' s remark ? 36S 
are nebulae classified? 370. Elliptic nebulae? a. The nebula in Andromeda. 



How 



266 NEBULA 



form, two dark clefts appearing to divide it longitudinally ; while its 
length, as viewed through this instrument by Prof. Bond, is 4°, and 



its breadth, 2^°. 

Fig. 123 




annttlar nebula in ltba. — 1. Sir John Herschel ; 2. Lord Rosse. 

371. Annular nebula are such as have the form of a 
ring. These are very rare, the heavens affording only four 
examples. 

a. The most remarkable one is found in Lyra, situated between 
the stars Beta and Gamma, and may be seen with a telescope of mod- 
erate power. It is slightly elliptical and has the appearance of a flat 
oval ring, the opening occupying somewhat more than one-half of the 
diameter. The central portion is not altogether dark, but is crossed 
with faint nebulous streaks, compared by some to gauze stretched over 
a hoop. The telescope of Lord Rosse shows fringes of stars at its 
inner and outer edges. (See Fig. 123.) The other annular nebulae are 
two in Scorpio, and one in Cygnus. 

372. Spiral Nebula are such as have the form of one 
or more spirals or coils ; in some cases presenting the 
appearance of continuous convolutions, or whorls ; in oth- 
ers, of great spiral arms or branches projecting from a central 
nucleus. 

a. The discovery of nebulae of this remarkable form is due to Lord 
Rosse, no indication of it whatever having been afforded by the great 

Questions. —371. What are annular nebulae ? Their number? «. The most remarka- 
ble ? 372. What are spiral nebula ? a. By whom discovered ? The most remarkable ? 
Describe the one in Leo. 



NEBULA. 267 

telescope of Sir William Herschel. The grandest object of this kind 
is found in Canes Venatici. Brilliant spirals, unequal in size and 
brightness, and apparently overspread with a multitude of stars, 
diverge from the central nucleus, the whole suggesting the idea, of a 
rotary movement of considerable rapidity, and the play of forces at 
which the imagination is startled when it contemplates the immensity 
of space filled by this wondrous object. 
Fig. 124. 




SPIB.VL NEBTTLJE IN LEO. — Lord JtoSSe. 

Figure 124 represents a very beautiful object of this kind in the lower 
jaw of Leo, the spiral form being clearly brought out in Lord Rosse's great 
telescope. The convolutions are nearly all closed, so as to assume almost 
the form of concentric ellipses, the central one containing what appear like 
several distinct stellar nuclei. 

373. Planetary Nebulae are those which, in their cir- 
cular or slightly elliptical form, their pale and uniform light, 
and their definite outline, resemble the larger and more dis- 
tant planets of our system. 

a. One of the most striking of this class is found in Ursa Major 
(near (3), the light of which, in Sir John Herschel's drawing, is quite 
uniform ; but when seen through Lord Rosse's telescope, it presents 
the appearance depicted in Fig. 125 (No. 1). The disc is about 3' in 
diameter, and exhibits a double luminous circle with two dark openings, 

Questions. — 373. "What are planetary nebulae ? a. What examples are given, and 
how described ? 



268 NEBULAE. 

each containing a bright but partially nebulous star. No. 2 in the 
same figure, represents a nebula near « (Kappa) in Andromeda, which, 
though perfectly round in Herschel's drawing, appears in Lord Rosse's 
like a luminous ring surrounded by a wide nebulous border. 

Fig. 125. 




PLANETABY NEBULA. 1, IN TJBSA MAJOB , 2, IN ANDEOMEDA. 

b. The number of planetary nebulae discovered is about 25, three- 
fourths of which are in the southern hemisphere. Several described by 
Sir John Herschel are of a blue color, in some cases with a tinge of 
green. 

c. The size of these objects must be amazingly great. That of 
Ursa Major, if no farther from us than the nearest star, a Centauri, 
would be sufficiently largi to fill a s^ace equal to three times the orbit 
of Neptune ; but there is reason to believe that it is more than 1,000 
times as large as this. How vast then must be the size of such a neb- 
ula as that in Andromeda ! 

In Fig 128, 1 and 2 are representations of planetary nebulae. The 
former is in Aquarius and is quite remarkable for its brightness. 

374. Stellar Nebulje are those which appear to envelope 
one or more brilliant spots or points, resembling stars sur- 
rounded by a nebulous border or ring. There are several 
varieties, the most important of which are nebulous stars. 



Questions. — b. Their number ? c. Size ? 374. What are stellar nebulae ? 






NEBULiE. 2C9 

375. Nebulous Staks are stars encircled by a nebulous 
border, which in some cases has a clearly defined outline, in 
others gradually shading off into the general appearance of 
the sky. 

Fig. 126. 






a. Such stars differ from other stars only in having this apparently 
nebulous atmosphere. If the nebula is circular the star occupies the 
centre of it ; while in the case of some that are elliptical, two stars are 
placed at the foci. 

In the above cut (Fig-. 126), No. 5 represents a remarkable nebulous star 
in Cygnus. The star is of the 11th magnitude, and is at the centre of a 
perfectly circular nebula of uniform light, and about 15' in diameter. No. 4 is 
a stellar nebula in Sobieski's Shield, of an elliptic form, and having two stars 
at the foci of the ellipse. These stars are described by Sir John Herschel 
as of a gray color. No. 3 is the representation of a nebula bearing a re- 
semblance to a comet. It is found in the tail of Scorpio. There are several 
other instances of such nebulas, which from their appearance are called 
conical or cometary nebula. In the case of each the stellar, or bright, point 
is at one extremity of the nebulous mass. 

b. It has been thought by some that the connection between these 
nebulae and stars is not real, but is merely the effect of perspective, the 
one being situated behind the other, but separated by a wide interval. 
It is, however, very improbable that so many of these nebulae should 
be found with stars placed exactly at their centres, some gradually be- 
coming fainter towards their borders, if there were no physical con- 
nection between them ; especially as, up to the present time, no 
difference in their proper motion has been discovered. 

c. It seems, therefore, probable that these are stars encompassed 
with very extensive atmospheres in the same way, perhaps, as the 
luminous centre of our system is enveloped in what we call the Zodical 

Questions — 375. Nebulous stars? a. How different from other stars? What ex- 
amples represented in Fig. 1^6 ? b. Is the connection between the star and nebula op- 
tical or physical ? c. Their probable nature ? 



270 



NEBULA. 



Light, the sun itself being in reality a nebulous star ; but the atmos- 
pheric envelopes of the other stars referred to must be vastly more 
extensive. The one in Cygnus, described above as 15' in diameter, and 
therefore extending 450'' beyond the central star, must, if the object 
is only as far from us as a Centauri, have an extent equal to fifteen 
times the distance of Neptune from the sun. 

376. Irregular Nebula are such as have no symmetry 
of form and scarcely any distinctness of outline, and are also 
remarkable for the diversity of brightness which they exhibit 
at different parts. 

a. Arago remarks of these diffuse masses of nebulous matter, that 
"they present all the fantastic figures which characterize clouds car- 
ried away and tossed about by violent and often contrary winds." The 
most remarkable of these objects are the following : 

Fig. 127. 







CRAB NEBULA IN TAURUS. — Lord RodSe. 



Questions.— 376. What are irregular nebulae? a. Their general appearance? 



NEBULA. 271 

1. The Crab Nebula in Taurus (Fig. 127). — This singular object has 
an elliptic outline in ordinary telescopes, but in Lord Rosse's great 
reflector it presents an appearance which has been fancifully likened 
to a crab or lobster with long claws. 

2. The Great Nebula in Orion. — This is probably the most magnifi- 
cent of all the nebulae. It is very irregular in form ; of immense 
extent, covering a surface more than 40' square ; and consists of 
patches varying considerably in brightness. Near the famous sextuple 
star Orionis, already described, it is very brilliant ; but other portions 
are quite dim, and some absolutely black. It was thought that por- 
tions of this nebula had been resolved into stars by the telescopes of 
Lord Rosse and Prof. Bond ; but the experiments of Messrs. Huggins 
and Miller with the spectroscope have proved conclusively the gaseous 
nature of this object ; the light from the brightest part of the nebula 
giving a spectrum of only three bright lines, indicating the presence 
of hydrogen, nitrogen, and a third substance unknown. The examina- 
tion of other portions gave similar results. 

3. The Great Nebula in Argo. — This is another very irregular and 
extensive nebula, covering a space equal to five times the disc of the 
moon. It contains a singular vacancy of an irregular oval form near 
the centre, and not very far from the variable star Eta. " It is not 
easy," says Sir J. Herschel, " to convey a full impression of the beauty 
and sublimity of the spectacle which this nebula offers as it enters 
the field of the telescope, ushered in as it is by so glorious a pro- 
cession of stars, to which it forms 

a sort of climax." This nebula is Fig ' 12a 

remarkably destitute of any indica- 
tions of resolvability. 

4. TJie Dumbbell Nebula (Fig. 
128.)— This object is found in Vul- 
pecula, and derives its name from 
its singular appearance as viewed 
through a telescope of moderate 
power. In Lord Rosse's telescope 
it assumes a form of less regu- 
larity, and appears to consist of in- dumb-bell nebula.— Herschel. 



Questions.— How is the Crab Nebula described ? The Great Nebula in Orion ? That 
in Argo ? Dumb-bell nebula ? 




272 



NEBFI^ 



numerable stars mixed with a mass of nebulous matter. These may 
be only centres of condensation. 

5. The Magellanic Clouds. — These are situated in the southern hem- 
isphere and not far from the pole, and are called sometimes Nubecula 
Major and Minor, or the Greater and Lesser Cloudlets. The former is 
in Dorado ; the latter in Toucan. These objects are distinguished for 
their great extent, the larger one covering a space of about 42 square 
degrees, and the smaller being of about one-fourth that extent, but of 
greater brightness. The telescope of Sir J. Herschel decomposed them 
into separate stars, star-clusters, and numerous distinct nebulae. In 
the larger cloud, Herschel counted 582 single stars, 46 star-clusters, and 
291 nebulae ; and in the smaller cloud, 200 single stars, 7 star-clusters, 
and 37 nebulae. In the immensity of their extent and the diversity 
of objects which they present, they are only comparable to that ap- 
parently greatest of all clusters, the Milky Way. 

377. Double Nebula are those which indicate by their 
close proximity to each other that they have a physical 
connection. More than 50 of such objects have been 
enumerated, the component nebulae of which are not more 
than 5' apart. 

Fig. 129 represents an object of this kind, found in Gemini. It is com- 
posed of two rounded masses, 



Fig. 129. 




DOTTKLE NEBULA. — Lord RotfSe 



Struve, D' Arrest, Hind, 



terminated by brilliant ap- 
pendages and enveloped in a 
nebulous mass, the whole sur- 
rounded by light luminous 
ares resembling fragments of a 
nebulous ring. 

378. Vakiable Neb- 
ula are those which un- 
dergo changes in appar- 
ent form and brightness. 
a. Several instances of 
such changes have been 
positively ascertained by 
and other distinguished astronomers. The 



Questions.— Magellanic Clouds? 377. What are double nebulae? 37a What are 
variable nebulas ? a. Instances ? 



NEBULA. 273 

great nebulae in Orion and Argo have exhibited undoubted varia- 
tions of a marked character. When Sir J. Herschel observed the latter 
in 1838, the star Eta was of the 1st magnitude and situated in the 
densest part of the nebula , but in 1867, an observer at Hobart-town, 
found it within the central vacuity, and only of the 6th magnitude. 
It is also stated that the vacuity is materially different in form from 
that repres3ntel by Herschel. Another observer at Madras confirms 
these statements, and adds that the nebula has varied considerably in 
brightness while under his own observation. 

Some of the smaller nebulae exhibit changes similar to those of the 
variable stars. In 1861, it was noticed by D'Arrest that one in Tau- 
rus had disappeared ; and circumstances indicated that this event had 
occurred in 1858. In December, 1861, the nebula reappeared, increased 
in brightness for several months, but in December, 1863, could not be 
found. Phenomena of a similar character were observed by Sir W. 
Herschel. Two stars, surrounded by circular nebulae in 1774, presented 
no traces of these envelopes in 1811. If these objects, as it was formerly 
supposed, were all composed of distinct stars, it would be scarcely pos- 
sible to conceive how such variations or disappearances could occur, 
particularly within the short periods mentioned ; but on the hypothe- 
sis that they consist of diffuse luminous matter, each nebula being a 
separate mass, these changes harmonize with what we see among the 
stars themselves. 

379. Structure of the Universe. — The universe has 
been supposed, by many modern astronomers, to consist of 
an infinite number of star-clusters similar to the galaxy, and 
situated at inconceivably immense distances from it and 
from each other. In view, however, of the recent discov- 
eries as to the nature of the nebulae proper, this hypothesis 
can not be considered as established ; and the true structure 
of the universe remains a problem to be solved. 

a. The hypothesis alluded to was a deduction from that which, sup- 
posing every nebula to be resolvable into stars, banished those that 
seemed irresolvable to the uttermost depths of space. Spectrum an- 
alysis having exploded this idea, we are necessarily compelled to 
discard those extravagant conceptions as to the distance of these visible 

Questions. — 379 Prevailing theory as to the structure of the universe? «. How 
affected by recent discoveries? What is proved by them? 



274 NEBULJS. 

objects. For, since we can not penetrate to the remotest parts of the 
galaxy, or resolve every portion of its milky light into stars, there is no 
reason for believing that those star-clusters, which are readily resolv- 
able, are beyond the confines of our sidereal system ; while the fact, 
already mentioned, that clusters and nebulae are invariably abundant 
where stars are rare, and as invariably wanting where stars abound, 
affords presumptive evidence that all these bodies are physically con 
nected with the same great system of the universe of which the galaxy 
itself is a portion. 

b. What other creations occupy the infinitude of space beyond the 
reach of human vision aided by the utmost efforts of optical and me- 
chanical skill, we can neither know nor perhaps conceive. There is 
reason for believing that light itself is gradually absorbed and thus 
extinguished in its journey ings from those remote regions of the uni- 
verse, long before it could reach our little orb and give us intelligence 
of the worlds from which it sped. But that the works of God are 
infinite in extent as they are in perfection and beneficent design, we 
can not but believe ; nor as we contemplate the wonders and glories 
of the starry heavens — those unfathomable abysses lit up by millions 
of suns, can we refrain from bowing in adoration and gratitude to 
Him who has endowed us with the intellectual power (far more won- 
drous than even these worlds themselves) to discover and survey 
their vastness and magnificence, and with those moral and spiritual 
capacities, by the due cultivation of which we may prepare ourselves 
for an existence in that future world where we shall be enabled, in a 
far higher degree, to contemplate His power and to understand His 
infinite wisdom and beneficence. 

Questions. — 6. Other creations in the infinitude of space ? Why not discoverable ? 
Feelings excited by a contemplation of the starry heavens ? 



APPENDIX. 



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276 



APPENDIX 



TABLE II. — ELEMENTS OP THE MINOR PLANETS. 



NAME. 


c 

3 


to 

c a 
S3 


a 
1 


o « 


^ o 
35 


Discoverer. 


ft 




8 
43 
71 
40 
18 
80 
12 
27 

4 
30 
52 
84 

7 

9 
62 
63 
25 
20 
67 
44 

6 
83 
21 
42 
19 
79 
11 
17 
46 
89 
29 
13 

5 
14 
32 
91 
47 
70 
54 
78 
23 
37 
15 
51 
66 
85 
26 
73 

3 

75 
77 


© , s=l 
2.2014 
2.2034 
2.2661 
2.2677 
2.2956 
2.2963 
2.3344 
2.3467 
2.3733 
2.3655 
2.3657 
2.3675 
2.3862 
2.3S66 
2.393 
2.395 
2.4008 
2.4097 
2.4217 
2.422 
2.4259 
2.4287 
2.4354 
2.44 
2.4411 
2.4431 
2.4519 
2.4735 
2.5265 
2.5498 
2.554 
2.5766 
2.5771 
2.586 
2.5873 
2.5958 
2.5959 
2.6133 
2.6197 
2.6228 
2.6271 
2.6414 
2.6437 
2.6491 
2.6512 
2.6536 
2.6561 
2.6666 
2.6684 
2.6698 
2.6719 


.157 

.168 

.12 

.046 

.217 

.2 

.219 

.173 

.09 

.126 

.066 

.238 

.231 

.123 

.185 

.126 

.254 

.144 

.1S5 

.151 

.203 

.084 

.162 

.225 

.158 

.195 

.099 

.128 

.164 

.18 

.074 

.087 

.187 

.166 

.083 

.237 

.183 
.204 
.205 
.232 
.177 
.187 
.287 
.158 
.191 
.087 
.043 
.257 
.307 
.136 


/ 

5 53 

3 28 
5 24 

4 16 

10 9 
8 87 

8 23 

1 35 

7 8 

2 6 

9 57 
9 22 

5 28 
5 36 

3 34 
5 47 

21 35 

41 

5 59 

3 42 

14 47 
5 2 

3 5 

8 34 

1 33 

4 37 

4 37 

5 36 

2 18 
16 11 

6 8 
16 31 

5 19 

9 8 
5 29 

8*"l 

11 38 
5 7 
8 38 

10 13 

3 7 

11 44 

2 48 

3 4 
11 53 

3 36 
2 25 
13 1 
5 
2 28 


Yrs. dys. 
3 97 
3 99 
3 150 
3 151 
3 174 
3 175 
3 207 
3 217 
3 229 
3 223 
3 223 
3 225 
3 240 
3 251 
3 256 
3 258 
3 263 
3 270 
3 280 
3 281 
3 284 
3 287 
3 292 
3 296 
3 297 
3 299 
3 306 

3 325 

4 6 
4 26 
4 80 
4 50 
4 51 
4 58 
4 59 

4* "67 
4 82 
4 88 
4 90 
4 94 
4 107 
4 109 
4 114 
4 116 
4 118 
4 120 
4 129 
4 181 
4 133 
4 134 


Hind 


1847 
ls57 
1861 
1856 
1852 
1864 
1850 
1853 
1807 
1854 
1858 
1865 
1847 
1848 
1860 
1861 
1853 
1852 
1861 
1857 
1847 
1865 
1852 
1856 
1852 
1863 
1850 
. 1852 
1857 
1866 
1854 
1850 
1845 
1851 
1854 
1866 
1857 
1861 
1853 
1S63 
1852 
1855 
1851 
1857 
1S61 
1865 
1853 
1862 
1804 
1862 


Ariadne 


Pogson 

('. H. P. Peters. 
Goldschmidt. .. 
Hind 


Harmon i a 

Melpomene ; 

Sappho 


Poffson 

Hind 


Euteepe 


Hind 




Olbers 




Hind 




Laurent 

Luther 

Hind 




Iris 

Metis 


Graham 

Ferguson 

De Gasparis 

Chacornac 

De Gasparis 

Poison 

Goldschmidt... 

Hencke 

De Gasparis 

Goldschmidt... 

Posson 

Hind 




Piiocea 

Massilia 

Asia 


Nysa 


Here 

Beatrix 


LUTETIA 


Isis 

FORTUNA... 


ElJKYNOME 

Parthenope ..... 


Watson 

De Gasparis 

Luther 

Pogson 

Stephan 

Marth 


IIestia 




Ampiiitrite 

EuERIA 

ASTR^EA 

Irene 

Pomona 


De Gasparis 

Hencke 

Hind 


Goldschmidt... 


Melete 


Goldschmidt. . . 






Hind 










De Gasparis 

Ferguson 

H. P. Tuttle . . . 






Io 


Proserpine 

Clytie 

Juno.... 




Tuttle 


Harding 

Peters . ... 









APPENDIX 



277 



ELEMENTS OF THE MINOR PLANETS — Contorted. 



NAME. 


£ 


Po- 
ll 


c 

o 
o 


a 

C 

s 


2 
O 


CO 


Discoverer. 




Angelina 

Circe 


64 
84 
58 
55 
60 
45 
38 
36 
72 
56 
82 

1 
39 
41 

2 
88 
74 
28 

81 
33 
48 
22 
16 
68 
59 
35 
£0 
86 
53 
49 
90 
61 
24 
10 
31 
57 
76 
65 
87 
92 
93 
94 
95 


®'s=l. 
2.6809 
2.6863 
2.7003 
2,7123 
2.7131 
2.7212 
2.7401 
2.7461 
2.7554 
2.7591 
2.7603 
2.7667 
2.7671 
2.7691 
2.7696 
2.7702 
2.7777 
2.7785 
2.7804 
2.8563 
2.8641 
2.8812 
2.9107 
2.9237 
2.9717 
2.9848 
3.0f66 
3.0825 
3.0908 
3.0999 
3.1094 
3.1188 
3.1297 
3.1431 
3.1511 
3.1527 
3.1565 
3.3S77 
3.4205 
3.4927 


.128 

.107 

.042 

.197 

.117 

.08 

.155 

.301 

.174 

.145 

.226 

.08 

.115 

.266 

.24 

.165 

.238 

.15 

.188 

.212 

.339 

.132 

.098 

.135 

.174 

.162 

.217 

.237 

.205 

.101 

.077 

.148 

.169 

.117 

.1 

.22 

.104 

.188 

.12 


o 

1 

5 
5 

11 

8 
6 
6 

18 

23 

7 

2 

10 

10 

15 

34 

5 

3 

9 

7 

7 

1 

5 

18 

3 

8 

18 

8 

8 

4 

7 

6 

2 

2 

3 
26 
15 
2 
8 


/ 

20 
26 

2 
47 
87 
35 
58 
42 
19 
14 
51 
36 
22 
59 
43 
15 
59 
21 
57 
£5 
56 


44 

4 
28 
15 
12 

9 
48 
25 
29 
16 
12 
49 
49 
27 

8 

2 
28 


Yrs. 
4 

4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
6 
6 
6 


dys. 

142 

147 

160 

171 

172 

179 

196 

201 

209 

213 

214 

220 

221 

223 

223 

224 

231 

232 

233 

302 

309 

325 

353 

45 
57 

78 
150 
158 
168 
176 
186 
196 
209 
217 
218 
222 

86 
119 
193 


Tempel 

Chacornac 


1S61 

1S55 
1860 
1858 
1860 
1857 
1856 
1855 
1861 
1858 
1S64 
1801 
1856 

M 

1802 
1866 
1S62 
1854 
1861 
1864 
1854 
1857 
1852 


Concordia 

Alexandra.... .. 


Goldsdimidt.. . 

Chacornac 

Goldschmidt.. . 

Chacornac 

Goldschmidt... 




Leda 


Atalanta 

Niobe 


Pandoea 




Luther 

Piazzi 

Chacornac 

Goldschmidt .. 
Olbers 


Ceres \ 


L.ETITIA 

Daphne 


Pallas 




Peters 

Tempel 

Luther 

Tempel 

Chacornac 

Luther 

Hind 


Galatea 






Terpischore 

Polyhymnia 






DeGasparis.... 
Schiaparelli.... 
Goldschmidt... 

Luther 

Goldschmidt.. . 

Tietjen 

Goldschmidt.. . 
it 


Hesperia ........ 


1861 
I860 


Leucothea 

Tales 


1855 
1857 


Semele 


1866 
1858 




185. 




186< 




Forster 


1S6( 




DeGasparis 

Ferguson 


185f 


Hygeia 

euphrosyne 

Mnemosyne 


184* 
185 
185 


D'Arrest 

Tempel 

Pi.gson 

"Watson 


180 




1S6 




18U 




ISO 


Undina 


u 


Watson 

Luther 


u 




« 

























83?" Melete was at first supposed by Goldschmidt to be Daphne, but was recog- 
nized to be a new planet on the calculation of its elements by Schubert in 1858. Hence 
its number is sometimes given as 56. 



INDEX 



Aberration of light, 245. 

Aerolites, 225. 

Algol, 257. 

Alignments, method of, 242. 

Altitude, 57. 

true and apparent, 59. 
Altitude of the pole, 59. 
Analemma, use of, Tl. 
Angle, 11. 

measurement of 12. 

of vision, 11. 
Annual equation of the moon, 180. 

parallax, 229. 
Annular eclipse, 139. 

nebulae, 266. 
Anomalistic year, 
Apogee, 112. 
Apparent motions of the heavenly bodies, 18 

of the inferior planets, 165. 

of the sun, 63. 

of the superior planets, 168. 
Argo, great nebula in, 271. 
Aspects of the planets, 43. 
Asteroids (see Minor Planets). 
Astraea, discovery of, 200. 
Atmosphere of Jupiter, 178. 

of Mars, 173. 

of the moon, 125. 

of Saturn, 185. 

of the sun, 107. 
August meteors, 224. 
Axial inclinations of the planets, 41. 

rotations of the planets, 40. 

velocity of Jupiter, 175. 
Azimuth, 57. 

Bailt'8 Beads, 40. 

Beer & Madler's charts, 125, 173. 

Belts, Jupiter's, 177. 

Saturn's, 185. 
Biela's comet, 211, 220. 
Binary Stars, 252. 
Bode' slaw, 39, 196. 
Brorsen's comet, 211. 

Cardinal points, how determined, 23. 

of ecliptic, 67. 
Celestial equator, 64 

latitude and longitude, 70. 
Central sun, 250. 



Centre of gravity of solar system, 20T. 
Centrifugal force, 29, 30, 88. 

law of, 1 75. 
Centripetal force, 29. 
Ceres, discovery of, 199. 
Chaldeans, 17, 140, 141. 
Chinese observations, 17, 130, 258. 
Circles, great and small, 15. 

of daily motion, 57. 
Civil day, 95. 
Clusters of stars, 260. 
Coal-sack, 247. 
Colored stars, 251. 
Colures, 67. 
Comet, Biela's, 220. 

Donati's, 222. 

Encke's, 21 S. 

Halley's, 216. 

of 1680, 216. 

of 1744, 212, 220. 

of 1811, 221. 

of 1843, 221. 

of 1844, 212. 

of 1861, 222. 

of 1862, 222. 
Comets, 209. 

direction of motion, 212. 

elements of, 211. 

elliptic or periodic, 211. 

nucleus of, 215. 

number of, 213. 

orbit& of, 209. 

size of, 213. 

tails of, 214. 
Comparative axial inclinations, 41. 

densities, 26. 

distances, 88. 

eccentricities, 34. 

magnitudes, 25. 

masses, 27. 

orbital velocities, 40. 

times of rotation, 42. 
Conic sections, 210. 
Conjunction, 43. 
Constant day and night, 74. 

at Jupiter, 176. 

at Mars, 172. 
Constellations, 231. 

catalogue of, 233. 

classification of, 232. 



2t0 



INDEX. 



Constellations, history of, 234. 

number of, 232. 

table for learning, 239. 
Copernican system, 18. 
Copernicus, a lunar mountain, 127. 
Corona, in solar eclipse, 140. 
Cotidal lines, 147. 
Craters, lunar, 127. 
Crystalline spheres, 20. 
Culmination, 56. 
Cusps, of Mercury, 153. 

of Venus, 153. 

D'Abeest's comet, 211. 
Day and night, 73. 
Declination, 67. 

circle of, 67. 
Degree, length of, 89. 
Densities of the planets, 26. 
Derivative tides, 147. 
De Vico's comet, 211. 
Difference of time, 51. 

of longitude, 51. 
Digits, 138. 

Dip of the horizon, 55. 
Distances of the planets, 37. 
Diurnal arc, 59. 
Donati's comet, 220. 
Double stars, 251. 

Eaeth, density of, 102. 

diameter of, 90. 

distance from the sun, 99. 

general form of, 49. 

rotation of, 17. 

size of, to find, 88. 

spheroidal form, 88. 
Earth's orbit, eccentricity of, 101. 

variation in, 86. 
Earthshine on the moon, 123. 
Eccentricity, 14 

of planets' orbits, 34. 

of stellar orbits, 253. 
Eclipse, first recorded, 141. 
Eclipses, 131. 

annular, 139. 

central, 138. 

cycle of, 139. 

number in a year, 135. 

phenomena of, 140. 

total and partial, 138. 
Ecliptic, 64. 

obliquity variable, 92. 
Ecliptic limits, 132, 133. 
Elements of a planet's orbit, 205. 

of a comet' s, 211. 
Ellipse, defined, 14. 

major and minor axes of, 14. 
Elliptic comets, 211. 

nebulae, 265. 
Elongation, 44. 

extreme, 150. 

of planets at Xeptune, 192. 
Encke's comet, 218. 
Epicycle, 31. 



Equation of the centre, 35. 

of time, 95. 
Equator, 50. 
Equinoctial, 64. 

spring tides, 146. 
Equinoxes, 64, 66. 
Establishment of the port, 147. 
Evection, 129. 
Evening and morning star, 47, 163. 

Facul-s, 105. 

Faye's comet, 211. 

Fire balls, 225. 

Fixed stars, 18. (See Stars.) 

Fizeau's experiments on light, 182. 

Foci, 14. 

Force, centrifugal, 29, 30. 

centripetal, 29. 

impulsive and continuous, 29. 

Galactic circle and poles, 248. 
Galaxy, 246. 
Galileo, 18, 104. ' 
Galle, Dr., finds Neptune, 186. 
Geocentric place, 205. 
Georgium Sidus, 192. 
Gravitation, law of, 29. 
how discovered, 30. 
Great inequality of Jupiter and Saturn, 206. 
Greek alphabet, 232. 

Halley's comet, 216, 217. 
Harvest moon, 117. 
Heliocentric place, 205. 
Herschel, Sir W., 183, 185, 190, 248, 250, 
253, 264. 

theory of solar spots, 107. 

nebular theory, 264. 
Herschel, Sir J., 34, 109, 153, 174, 177, 271. 
Horizon, 54. 

dip of, .55. 

rational, 55. 
Horizontal parallax, 60. 
Horrox, 163. 
Hour angle, 67. 

circle, 67. 
Hourly motions of the planets, 40. 
Humboldt, 110,223. 
Hunter's moon, 118. 
Hyperbola, 210. 

Inclination of orbit, 36, 37. 

of axis, 41. 
Inequalities, 204. 

Inequality of Jupiter and Saturn, 206. 
Inertia, 146. 
Inferior planets, 149. 

Juno, discovery of, 199. 

Jupiter, 174. 

Jupiter's satellites, 178. 

eclipses of, 180. 

libration of, 181. 

Kepleb's laws, 30, 33. 



INDEX 



281 



Kepler's 3d law, applied, 158, 169. 
Kepler's star, 259. 

Laplace, 130, 143, 181, 206. 
Lassell, 23, 186, 188, 197, 257. 
Latitude and longitude, 49. 
Law, Bode's 39, 196. 

of oblateness, 175. 
Laws, Kepler's, 30, 33. 
Lexell's comet, 220. 
Librations of the moon, 121. 
Light and heat at Jupiter, 177. 

Mercury, 154. 

Neptune, 197 

Saturn, 184. 
Light, aberration of, 245. 

extinction of, in space, 274 

intensity of, at different planets, 109. 

solar, comparative intensity of, 109. 

velocity of, 182. 
Limits, ecliptic, 132, 133. 

transit, 155. 
Longest day and night, 76. 
Longitude, 49. 

how found, 182. 
Lost or missing stars, 260. 
Lunar axis, position of, 122. 

inclination of, 122. 
Lunar day and night, 123. 
Lunar mountains, 126. 

height of, 127. 

eclipses, 135. 
Lunar irregularities, 128. 

theory, 130. 
Lunation, 116. 

Maples' s chart of Mars, 173. 

of the moon, 125. 
Magellanic clouds, 272. 
Major and minor axes, 14. 
Mars, 168. 

distance found by phases, 169. 

parallax of, how found, 171. 

ruddy color of, 174. 

polar hemispheres of, 173. 
25. 

of earth and sun, 102. 

of the planets, 27. 

of sun and planets, how to find, 207. 

of Sirius, 254. 
Mean and true place, 35. 
Mercury, 149. 

mass of, 151, 219. 

mountains in, 153. 

transits of, 155. 
Meridian of a place, 56. 
Meridian circles, 50. 

length of a degree of, 89. 
Meridian altitude of the sun, 66. 
Meteoric dust, 227. 

epochs, 224. 

rings or streams, 224 

satellites of 'the earth, 226. 

transits, 227. 

theory of sun's heat, 111. ' 



Meteoric theory of minor planets, 228. 
Meteors, 223. 

August, 224. 

cosmical origin of, 225. 

November, 227. 

number of, 225. 

physical origin of, 228. 
Milky Way, 246. (See Galaxy.) 
Million, idea of, 38. 
Minor planets, 199. 

magnitude of, 26, 201. 

mass of, 26. 

origin of, '.02. 

principal discoverers of, 200. 
Mira, the wonderful star, 257. 
Moon, 112. 

harvest, 117. 

librations of, 121. 

phases of, 114. 

synodic and sidereal periods of, 116. 
Moonlight, in winter, 118. 

in polar regions, 118. 
Morning and evening star, 217. 
Motion, laws of, 28. 

curvilinear, 29. 

resultant, 29. 
Mutual attractions of the planets, 202. 

Nadir, 56. 

Nasmyth's " Willow Leaves," 107. 

Nebular hypothesis, 202. 

theory of Herschel, 264 
Nebula in Andromeda, 265. 

in Argo, 271. 

in Lyra, 266. 

in Orion, 271. 

(Jr. b, Vlii 

Dumb-bell, 271. 
Nebulae, 2G3. 

annular, 266. 

cometary, 269. 

double, 272. 

elliptic, 265. 

irregular, 270. 

planetary, 267. 

resolvable and irresolvable, 264. 

spiral, 266. 

stellar, 268. 

variable, 272. 

gaseous nature of, 264. 

where abundant, 265. 
Nebulous stars, 269. 
Neptune, 194 

discovery of, 195. 

satellite of, 197 

supposed ring, 19T. 
Newton, 30, 34, 144 ' 
Nocturnal arc, 59. 
Nodes, 36. 

November meteors, 227. 
Nutation, 244 * " . 

how discovered, 245. 

solar and lunar, 245. 

Oblateness. of the earth, 90. 
law of, 175 



282 



INDEX, 



Oblique sphere, 58. 
Obliquity of the ecliptic, 65. 

variation in, 92. 
Occupation, 141. 
Olbers, 199, 200 

theory as to asteroids, 202. 
Opposition, 43. 
Orbits, planetary, 28-37. 

eccentricity of, 34. 

inclination of, 36. 

of comets, 20, 210. 

of meteors, 22T. 

of satellites, 180, 190. 

of stars, 253, 254. 

Pallas 199. 

Parabola, 210 

Parallactic inequality, lunar, 130. 

Parallax, 59. 

of the moon, 60, 112. 

of the sun, 164, 171. 

of the stars, 229, 254 
Parallel sphere, 53. 
Parallels of latitude, 51. 
Pe ldulum, a measure of gravity, 88. 
Penumbra, 131. 
Perigee, 112. 
Periodic comets, 211. 

meteors, 223. 

stars, 253. 

times of the planets, 39. 
Perpetual apparition, circle of, 58. 

occultation, circle of, 59. 
Perturbations, 204 
Phases of Mars, 168. 

of the moon, 114. 

of Venus, 156. 
Phenomena of the heavenly bodies, IT. 
Photosphere of the sun, 107. 
Plane, defined, 10. 
Planetary nebulae, 267. 
Planets, 20. 

comparative densities, 26. 

elements of orbits, 205, 

major and terrestrial, 25. 

masses of, 27. 

mutual attractions of, 204. 

orbital eccentricities, 34. 

orbital inclinations, 37. 

orbital velocities, 40. 

relative distances, 38. 

rotations, 41. 
Pleiades, 243. 
Polar circles, 76. 
Polaris (see Pole-star). 
Poles, of a circle, 15. 

galactic, 243. 

terrestrial, 50. 
Pole-star, 244. 
Positions of the sphere, 58. 
Praesepe, 261. 
Precession of the equinoxes, TO. 

cause of, 90. 

effect of, 91, 244. 

lunar, 122. 



Prime meridian, 50. 

vertical, 57. 
Priming and lagging of the tides, 147. 
Primitive tides, 147. 
Problem of Three Bodies, 204. 
Problems for the globe, 52, 7o, 79, 1)6, £41. 
Ptolemaic system, 18. 
Ptolemy, 18, 129, 238. 
Pythagoras, 18. 

QUADBATUBE, 144. 

Quartile, 45. 

Questions for exercise, 43. 

Radiating streaks on the lunar disc, 127. 
Radius- vector, 32. 
Refraction, 61. 

amount at different altitudes, 63. 

effect of, 62. 

effect in a lunar eclipse, 141. 
Resisting medium, 217. 
Resolvable nebulas, 264. 
Retrogradation, arc of, 169. 

duration of, 169. 
Retrograde motion. 163. 
Right ascension, 67. 

sphere, 58. 
Ring mountains, lunar, 12T. 
Rings, meteoric, 224. 

of Saturn, 185. 
Roemer, 182. 
Rotation of nebulae 266. 

planets, 42. 

Saturn's rings, 18T. 

satellites. 190. 

stars, 257. 

sun, 42. 

Satellite of Neptune, 19T. 

of Sirins, 251, 255. 
Satellites of Jupiter, 178. 

Saturn, 189. 

Uranus, 23, 194. 
Saturn, 182. 

belts of, 185. 

celestial phenomena at, 190. 

density, 184. 

equatorial velocity of, 184. 

mass, 184. 

oblateness, 183. 

rings, 185-189. 

satellites, 189, 190. 

telescopic view of, 187. 
Schroeter, 153, 159. 

Schwabe's researches on solar spots, 106. 
Secondary circles, 50. 

planets (see Satellites). 
Secular acceleration, lunar, 130. 

perturbations, 204. 

Variations, 205. 
Seasons, 82. 

length of, unequal, 84 
variable, 86. 
Selenograpy, 124 
Sextile, 45. 



INDEX, 



Shadow, earth's, 131. 

moon's 137. 
Shooting stars (see Meteors). 
Sidereal day, 92. 

month, 116. 

year, 96. 

period of Jupiter, 175. 
Mars, 172. 
Mercury, 154. 
moon, 116. 
Neptune, 196. 
Saturn, 183. 
Uranus, 193. 
Venus, 162. 
Signs of the ecliptic, 68. 

of planets (see each). 
Sine of an angle, 101. 
Snow and ice at Mars, 173. 
Solar day, 93. 

eclipses, 135. 

heat, theory of, 111. 

light, intensity of, 109. 

parallax, 163, 171. 

spots, 103-108. 

system, 18. 

motion of, 250. 
Solstices, 64. 
Spectrum analysis, 255. 
Sphere, defined, 14. 

positions of, 58. 
Spheroid, oblate and prolate, 16. 
Stability of Saturn's rings, 187. 

solar system, 207. 
Stars, 229. 

apparent places of, 244. 

binary, 252. 

colored, 251. 

double, 251. 

distance of, 230. 

list of principal, 240. 

lost or missing, 260. 

magnitudes of, 230. 

multiple, 250, 256. 

names of, 232, 240. 

nebulous, 269. 

new, 258. 

parallax of, 229. 

physical constitution of, 255. 

proper motion of, 229. 

scintillation of, 229. 

shooting or falling, 223. 

temporary, 260. 

variable, 257. 
Star clusters, 260. 

conflagration of a, 259. 

figures, 241 

groups, 261. 

Kepler's, 259. 

names, 240. 

showers, 223. 

Tycho's, 25S. 
Stationary points, 167-169 
Structure of the universe, 273. 
Sun, 100. 

a small star, 255. 



Sun, a nebulous star, 270. 

apparent and real diameters of, 101. 

apparent motions of, 63, 64. 

apparent magnitude, 209. 

distance from the earth, 99. 

inclination of axis, 104. 

mass, 102, 207. 

meridian altitude, 66. 

motion of, in space, 109, 250. 

photosphere of, 107. 

physical constitution of, 107. 

surface and volume, 102. 
Sun's heat and light, 111. 
Superficial gravity at Jupiter, 176. 

Mercury, 153. 

Saturn, 184. 

Venus, 159. 
Superior planets, 168. 
Synodic period, 45. 
Syzygies, 115. 

Telescope, invention of, 20. 
Telescopic views of Jupiter, 178. 

of the moon, 125. 

of Saturn, 187. 
Temporary stars, 260. 
Thales, 140. 
Theory, meteoric. Ill, 229. 

of nebulae, 264. 

of solar spots, 107. 

of zodiacal light, 111. 
Theta Orionis, 256. 
Three Bodies, problem of, 204 
Tidal force of sun and moon, 143. 
Tides, cause of, 142. 

equinoctial spring, 144. 

flood and ebb, 142. 

height of, 145, 148. 

highest, 148. 

how retarded, 146. 

of rivers and lakes, 148. 

priming and lagging, 147. 

primitive and derivative, 147. 

why they rise later, 146. 
Tide, waves, 140. 

velocity of, 148. 
Time, 92. 

equation of, 95. 
Transits, meteoric, 227. 

of Jupiter's satellites, 180. 

of Mercury, 155. 

of Titan, 190. 

of Venus, 163. 
Trapezium of Orion, 256. 
Triangle, defined, 13. 
Trine, 45. 
Tropics, 74. 
Twilight, 77. 

Twinkling of the stars, 229. 
Tycho Brahe, 258, 264 
Tycho, a lunar mountain, 127. 

Umbea, 131. 
Uranus, 191. 

elongation of planets at, 192. 



284 



INDEX, 



Uranus, existence predicted by Clairaut, 
218. 
satelites of, 23, 194. 
sunrise aud sunset at, 192. 

Variable nebulae, 272. 

stars, 257. 
Variation, lunar, 120. 

of obliquity of ecliptic, 92. 

in length of seasons, 86. 
Velocity of solar system, 110, 250. 
Velocities of planets, 40. 
Venus, 156. 

atmosphere of, 160. 

mountains in, 159. 

when most brilliant, 158. 
Vertical circles, 56. 

sun, 74. 
Vesta, 199. 
Visual angle, 11. 
Volumes of sun and planets, 24. 
Vulcan, 22, 149. 



Wilson's theory of sun's spots, 107. 
Winnecke's comet, 211. 
Wolfs researches on sun's spots, 106. 
Wollaston's estimate of sun's light, 109. 
discovery of lines in solar spectrum, 
256. 
Wright's theory of the Universe, '248. 

Yeah, anomalistic, 97. 
civil, 96. 

equinoctial or solar, 96. 
sidereal, 96. 
tropical, 96. 

Zenith, 56. 
Zenith distance. 57. 
Zodiac, 68. 

constellations of, 233. 
Zodiacal light, 110. 

cause of, 111. 

theory of Chaplain Jones, 110. 

theory of 1'rof. Norton, 111. 
Zones, 87. 






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Progressive Higher Arithmetic : combining the 

Analytic and Synthetic Methods, and forming a complete Treat- 
ise on Arithmetical Science, in all its Commercial and Business 
Applications, for Schools, Academies and Commercial Colleges. 



2 JJOBIN'SON'S SERIES OF MATHEMATICS. 

Particular attention has been given to the preparation of those 
subjects, which are absolutely essential to make good accountants 
and commercial business men. 

The different kinds of United States Securities are described, the 
difference between gold and currency, and the corresponding difference 
in prices exhibited in trade, are tauyht and illustrated ; also, a full 
Treatise of the Metric System of Weights and Measures has been 
added. 

Arithmetical Examples. This book contains 

nearly 1,500 Practical Examples, promiscuously arranged, and 
without the answers given, involving nearly all the principles 
and ordinary processes of common arithmetic, designed tho- 
roughly to test the pupil's judgment ; to cultivate habits of patient 
investigation and self reliance ; to test the truth and accuracy of 
his own processes by proof; in a word, to make him independent 
of a text-book, written rules and analysis. 

This work is not designed for beginners, but for those who have 
acquired at least a partial knowledge of the theory and applications 
of numbers from some other work, and it may be used in connection 
with any other book, or series of books on this subject, for Review 
or Drill Exercises. 

An edition is printed exclusively for teachers, containing the 
answers at the close of the book. 



New Elementary Algebra: a clear and practical 
Treatise adapted to the comprehension of beginners in the 
Science. The introductory chapter is designed to give the 
pupil a correct comprehension of the utility of symbols, and of 
the identity and chain of connection between Arithmetic and 
Algebra, leading him by easy and successive steps, from the study 
of written arithmetic to the study of mental and written algebra. 

New University Algebra, containing many new and 
original Methods and Applications both of Theory and Practice, 
and is designed for High Schools and Colleges. 

This book is not revision, but a newly prepared and recently 
published work, thoroughly scientific and practical in its discussions 
and applications, [t is a book filled with gems, and most of them 
original with the author. 



KOBINSOFS SERIES OF MATHEMATICS. 

Kiddle's NEW Manual of the Elements of 
Astronomy, Comprising the latest discoveries and 
theoretic views, with directions for the use of the Globes, and for 
studying the Constellations. 

The Publishers offer this work to accompany " ROBINSON'S 
MATHEMATICAL SERIES." 

The plan of the work is objective ; the illustrations are new and 
copious; the methods greatly simplified; the numerical calcu- 
lations, which are based on the recent determination of the Solar 
parallax, are made without recourse to any other than Elementary 
Arithmetic, and the most rudimental principles of Geometry. 

The book is designed for use in Normal Schools, Academies, 
High Schools, Seminaries, and advanced classes in Grammar 
Schools; and it is hoped that in this work the thorough and prac- 
tical Teacher will find a desideratum long sought for in this depart- 
ment of science. 

University Astronomy. Descriptive, Mathemat- 
ical, Theoretical and Physical ; designed for High Schools and 
. Colleges. Large 8vo 

JVew Geometry , bonnd separate, in cloth. 

Plane and Spherical Trigonometry , in sepa- 
rate volume, cloth. 

Concise Mathematical Operations. Being a 

Sequel to the author's Class-books, with much additional matter. 

Key to Geometry and Trigonometry, Sur- 
veying and Navigation. 

Key to Analytical Geometry, Differential 
and Integral Calculus, with some additional 

Astronomical Problems in the same volume. 

Keys to the Arithmetics and Algebras, are 

published for the use of Teachers. 



KOBmSOiTS SERIES OF MATHEMATICS. 

In it will be found condensed and brief modes of operation, not 
hitherto much known, or generally practiced, and several expedients 
are systematized and taught, by which many otherwise tedious 
operations are avoided". 

Brevity and perspicuity, two rare and commendatory excellences 
in a text-book, are leading features to this work, and, at the same 
time, the rationale of every operation, and the foundation of every 
principle, are fully and clearly shown. 

The design throughout has been, not to conceal, but fully to reveal 
the difficulties of the science, and to encourage the learner, not to 
avoid, but to grapple with, and to overcome them; since, to the 
student of Mathematics labor rightly directed, is discipline, and 
discipline, after all, is the true end of education. 

Wetv Geometry and Trigonometry, embracing 
Plane and Solid Geometry, and Plane and Spherical Trigono- 
metry, with numerous practical Problems, the whole newly 
illustrated. New and original demonstrations of some of the 
more important principles have been given, and the practical 
problems and applications, both in the Geometry and the Trigo- 
nometry, have been greatly increased. 

New Surveying and Navigation. With use of 

Instruments, essential Elements of Trigonometry, Mensuration, 
and the necessary Tables, for Schools, Colleges, and Practical 
Surveyors. 

The arrangement of the work, including as it does Trigonometry 
and Mensuration, requires that two terms should be employed in its 
completion, but students familiar with these subjects, by omitting 
them, can readily master the subject of Surveying proper in one 
term. 

New Conie Sections and Analytical Geo- 
metry /- prepared for High Schools and Colleges. 

New Differential and Integral Calculus; 

adapted for use in the High Schools and Colleges of the country — 
thorough and comprehensive in its character ; and while it does 
not cover the whole ground of this branch of Mathematics, yet 
so far as the subject is treated, it is progressive and complete. 

It is confidently believed that in literary and scientific mem., 
this work is not equalled by any similar production published in thif 
country. •■--.■■, 



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